The questions is not as straight forward as it appears and I have limited my response as much as I can.
Simple answer very unlikely Deuteronomy 18:15-18 relate to Jesus – as he is nothing like Moses
Deuteronomy 18:15-18 (NKGV)
15 “The LORD your God will raise up for you a Prophet like me from your midst, from your brethren. Him you shall hear, 16 according to all you desired of the LORD your God in Horeb in the day of the assembly, saying, ‘Let me not hear again the voice of the LORD my God, nor let me see this great fire anymore, lest I die.’
17 “And the LORD said to me: ‘What they have spoken is good. 18 I will raise up for them a Prophet like you from among their brethren, and will put My words in His mouth, and He shall speak to them all that I command Him.
Deu 18 - relates to a prophet, to come, a great prophet of high status (Moses, Abraham etc),from the brethren, who will only speak of what he is told, not of his own accord.
For the prophecy to be fulfilled all the aspects need to be relevant, not only parts.
The first point that needs to be clarified, is Jesus - Son of God / God or a mere prophet (human) albeit of high status chosen by God, but still a human. Even if he came as a human, if he is God or son of God he cannot be human or prophet. [Numbers 23:19, Hosea 11:9, 1 Samuel 15:29] These confirms that God is not human. So if Jesus is God he cannot be human & if he is son of God at best he can only be half human (Mary) & half God.
There is an argument that God could appear as a human or even become a human, certain verses have serious translation issues and figurative speech and would be contradictor to the below;
Job 25:4-6 4 How then can man be justified with God? or how can he be clean that is born of a woman? 5 Behold even to the moon, and it shineth not; yea, the stars are not pure in his sight. 6 How much less man, that is a worm? and the son of man, which is a worm?
Malachi 3:6 "For I [am] the LORD, I change not; therefore ye sons of Jacob are not consumed.
He cannot be Son of God or God but a prophet, a man at the same time. The argument that Jesus said he is a prophet would imply that he can surely not be son of God / God. You cannot have it both ways.
Brethren
There is an argument that brethren can refer to the Israelites, but as below we can see that it could also refer to the Ishmaelite's. Arabs being the brethren of the Jews.
If it was Isaiah or Jesus - would likely read “from among thee and thy children.”
Brethren has been elaborated in Genesis 16:12 “ And he will be a wild man; his hand will be against every man, and every man's hand against him; and he shall dwell in the presence of all his brethren.” – this relates to Ishmael – based on few passages
Genesis 25:9 “And his sons Isaac and Ishmael buried him in the cave of Machpelah, in the field of Ephron the son of Zohar the Hittite, which is before Mamre;” imply that Ishmael and Isaac lived together and were present at the time Abraham passed away.
Genesis 25:18 “And they dwelt from Havilah unto Shur, that is before Egypt, as thou goest toward Assyria: and he died in the presence of all his brethren” - this verse tells us that Ishmael died in the presence of his brethren.
Matt 21:43 - Therefore I tell you, the kingdom of God will be taken away from you and given to a people producing its fruits.
Isaiah 42:10 below ‘new song’
The above two seem to imply something different to previous - elaborated further below.
From your midst / from among you
Acts 3:22 “For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you.”
No mention of from the midst of thee
See different versions below;

Like unto thee
Deuteronomy 34:10 10 But since then there has not arisen in Israel a prophet like Moses, whom the LORD knew face to face.
Isaiah 28:11 - 11 For with stammering lips and another tongue He will speak to this people, (meaning a different language)
Jesus Completely different to Moses
i) Moses got married & had children
ii) Moses had natural birth not a miraculous birth
iii) Moses a mere man Not son of God
iv) Moses died a natural death.
v) Moses fought wars, spiritual and political leader,
vi) Jesus died on the cross
vii) Jesus resurrected
viii) Moses liberated Israelites from the yoke of Pharaoh
ix) Moses by and large accepted by his people – Jesus was not
x) Sermon on the mount was not new laws or a new covenant Matt 5:17 to fulfill the laws that came before.
xi) Miracles – many in the bible preformed miracles
xii) Moses received the Torah / Law – Jesus did not give any laws
xiii) Jesus laid no claim to a new Law; his disciples regarded the Law as a curse.
'And the Law is not of faith: but, The man that doeth them shall live in them. Christ hath redeemed us from the curse of the law'. (Galatians 3:12-13)
other verses that assist Deu 18 to show another prophet other then Jesus
John 1:19-27 19 Now this was John’s testimony when the Jewish leaders in Jerusalem sent priests and Levites to ask him who he was. 20 He did not fail to confess, but confessed freely, “I am not the Messiah.” (note this would be Jesus) 21 They asked him, “Then who are you? Are you Elijah?” He said, “I am not.” “Are you the Prophet?” (this clearly implies another prophet)
John 7:40 “ Many of the people therefore, when they heard this saying, said, Of a truth this is the Prophet
John 15:26 - 26 “When the Advocate comes, whom I will send to you from the Father—the Spirit of truth who goes out from the Father—he will testify about me.
(Jesus is talking about sending someone, clearly not him and not holy spirit (HS is truth, guidance strength etc…) also HS has been there since beginning and continuously in the bible)
John 16:7-8 7 But very truly I tell you, it is for your good that I am going away. Unless I go away, the Advocate will not come to you; but if I go, I will send him to you. 8 When he comes, he will prove the world to be in the wrong about sin and righteousness and judgment:
John 16:13 13 But when he, the Spirit of truth, comes, he will guide you into all the truth. He will not speak on his own; he will speak only what he hears, and he will tell you what is yet to come.
John 14:16 16 And I will ask the Father, and he will give you another advocate to help you and be with you forever (another / new not HS already hear of a person already hear)
John 14:30-31 30 I will not say much more to you, for the prince of this world is coming. He has no hold over me, 31 but he comes so that the world may learn that I love the Father and do exactly what my Father has commanded me. (someone coming not here already)
John 14:26 26 But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you.
Luke 3:16 16 John answered them all, “I baptize you with water. But one who is more powerful than I will come, the straps of whose sandals I am not worthy to untie. He will baptize you with[b] the Holy Spirit and fire. (will come – Jesus was already here)
Mark 1:7 7 And this was his message: “After me comes the one more powerful than I, the straps of whose sandals I am not worthy to stoop down and untie.
Acts 3:22 (NKJV) - 22 For Moses truly said to the fathers, ‘The LORD your God will raise up for you a Prophet like me from your brethren (brethren being Isaac & Ishmael sons of Abraham). Him you shall hear in all things, whatever He says to you.
Genesis 21:13 (NKJV) - 13 Yet I will also make a nation of the son of the bondwoman, because he is your seed.” - (regarding Ishmael)
Deuteronomy 33:1-2 (NKJV) - Moses’ Final Blessing on Israel
33 Now this is the blessing with which Moses the man of God blessed the children of Israel before his death. 2 And he said: “The LORD came from Sinai, And dawned on them from Seir; He shone forth from Mount Paran, And He came with ten thousands of saints; From His right hand Came a fiery law for them.
Isaiah 29:11-12 (NKJV) – 11 The whole vision has become to you like the words of a book that is sealed, which men deliver to one who is literate, saying, “Read this, please.” And he says, “I cannot, for it is sealed.” 12 Then the book is delivered to one who is illiterate, saying, “Read this, please.”
And he says, “I am not literate.”
[Jesus was not illiterate & never had a book, the bible came much later]
Isaiah 42:1-11 talks about another elected by God – clearly not Jesus
2 He will not cry out, nor raise His voice, Nor cause His voice to be heard in the street. 4 He will not fail nor be discouraged, Till He has established justice in the earth; And the coastlands shall wait for His law.”
10 Sing to the LORD a new song, And His praise from the ends of the earth, You who go down to the sea, and all that is in it, You coastlands and you inhabitants of them!
11 Let the wilderness and its cities lift up their voice, The villages that Kedar inhabits. Let the inhabitants of Sela sing, Let them shout from the top of the mountains.
***[clearly the above does not relate to Jesus]
[Kedar was the son of Ishmael]
Habakuk Chapter 3 verse 2-4 …2O LORD, I have heard the report of You; I stand in awe, O LORD, of Your deeds. Revive them in these years; make them known in these years. In Your wrath, remember mercy! 3God came from Teman, and the Holy One from Mount Paran. Selah His glory covered the heavens, and His praise filled the earth. 4His radiance was like the sunlight; rays flashed from His hand, where His power is hidden.…
Note: few final points
- Malachi – arguably Elijah
- the Messiah, nor Elijah, nor the Prophet?” (John 1:19-25) – clearly 3 people (someone else other than Jesus & Elijah & not him JtB)
- Elijah not a Brethren but from amongst as was Jesus
- Matthew 17:12 ‘…Elijah has already come, and they did not recognize him,….’ –
- John the Baptist (JtB) says - Mark 1:7 7 And this was his message: After me comes - (Elijah already come as above talking about someone else to come)
- Luke 3:16 – ‘…will come…’ again after JtB – Jesus hear and Elijah already come
- John 16:7-8 – ‘...Unless I go away, the Advocate will not come to you;…’ (Jesus talking about someone else to come after him as do the various other verses of John will come / will send)
conclusion - very unlikely that this relates to Jesus too many inconsistences and Jesus cannot fulfil all the aspects of the prophecy. even if you accept he like Moses a prophet, a man and could do miracles, there are more dissimilarity