The Idea in Brief
As was in the case of Balaam, who was not able to bring magical powers to bear on the people of God, the dark power instead lay in tempting and dissuading people from the Lord through idolatry and immorality, which is how Balaam brought the Israelites out from under the protection of the Lord (Numbers 22-25). In the end, Balaam had exploited the Israelites through this deception, and thus aggrandized himself.
In this same regard, the female prophetesses during the siege of Jerusalem had tempted and dissuaded the Israelites when they sold magical amulets and head scarfs, which brought the Israelites from under the protection of the Lord. That is, these charms were literal substitutes for the binding of the law on the heart (hand) and mind (head). Finally, the prophetesses had exploited the Israelites through this deception, and thus aggrandized themselves.
The Book of Deuteronomy mentions the heart and mind as the place for the Law of the Lord. That is, the hand stood for the heart, and the head stood for the mind.
Deut 6:5-8 (NASB)
5 You shall love the Lord your God with all your heart and with all your soul and with all your might. 6 These words, which I am commanding you today, shall be on your heart. 7 You shall teach them diligently to your sons and shall talk of them when you sit in your house and when you walk by the way and when you lie down and when you rise up. 8 You shall bind them as a sign on your hand and they shall be as frontals on your forehead.
With regard to Ezek 13:18, Rabbi Shlomo Yitzchaki ("Rashi") had understood that there were clear references to divination and witchcraft. His commentary makes several allusions to divination evident in this passage. His references to cushions and pillows under the arms finds no support with Keil & Delitzsch (1996), who lean toward the normal and plain reading of the text, which is that the false prophetesses had sold devices for binding the hands and fixing some firm head covering to the head.
In line with the plain and normal reading of the text, Rabbi Meïr Leibush ben Yehiel Michel Wisser ("Malbim") in the Nineteenth Century made the poignant and insightful observation that the amulets and veils in the verse were the analog to the tefillin and/or phylacteries, which were to represent the Law of Moses on the heart and mind (that is, on the hand and head). Thus the "magical" charms appear to be substitutes for the Covenant of Moses, which were to be affixed on the hand and head (that is, on the heart and mind per the verse from Deuteronomy, noted above). The following proposed translation comes from the first paragraph of the commentary of Malbim regarding this passage (which hyperlink is best viewed in Google Chrome).
Woe to the women who sew bands...
In like manner, [there is] the sanctity of putting tefillin on the hand against the heart in order to subject the desire and intents of the heart toward the Lord, and they place upon the head as over against the brain in order to enslave the power of thinking, and having in mind toward himself to bless himself. Thus there were female witches [with their analog amulets and veils].
The Babylonian Talmud makes several references to the tefillin and/or phylacteries. The most explicit is Menachot Folio 34b, which is best translated by Jacob Neusner. Jewish oral tradition recognizes the use of tefillin or phylacteries throughout Jewish history. The Jewish Encyclopedia mentions several ancient references, which include their first apparent use as early as the time of Elisha.
Finally, the translation of the Targum Jonathan (Aramaic translation of the Hebrew Bible) provides insight as to how Jewish scholars in the early centuries of this era had understood this particular verse in Hebrew. Please note the "patches of darkness" to emphasize the "magical" aspect of these charms.
Ezek 13:18 (Proposed Translation)
18 And you will say, so says the Lord God, "Woe upon them, since they were sewing patches of darkness upon all the joints of the hands, and were making scarves for the head of every sort in order to destroy souls. Will you (feminine plural) indeed be able to overpower my people in order to destroy (them) and prevail? Is it not their (=prophetesses-feminine plural) souls for destruction? Will they (=prophetesses-feminine plural) not indeed be overpowered from making covenants?"
The Aramaic term for covenant here is קְיָים, which is similar to the Aramaic word here for stand up or prevail, which is קוּם. Both words occur in this verse with the smallest of Aramaic letter, yod, distinguishing their respective meanings. In other words, the Targum translators drew the contrast between casting spells through the use of "magic" charms and self-aggrandizement (or prevailing to exploit people), which will NOT succeed according to this verse in the Targum. This Targum translation eliminates ambiguity that "magical" power would ever be stronger than the protection of the Lord. That is, there are no doubts that the Lord and his power are stronger than any "magical" power.
The emphasis here is protection under Covenant. Through their deliberate violation of the Covenant of Moses through idolatry, the history of the Israelites indicates how they squandered their divine protections. For example, during the siege of Jerusalem, rejection of the Mosaic Covenant appeared when Israelites paid false prophetesses to provide magical charms. These amulets and scarves "replaced" the Law of Moses, which was supposed to be tied on the heart and mind (that is, the hand and the head through tefillin and/or phylacteries). In this regard, the mystical charms of the false prophetesses had power not through any spiritual "magic" per se, but in their ability to leverage idolatry in order to tempt and dissuade people from relying upon the power of the Lord and his Covenant.
Keil, C. F., & Delitzsch, F. (1996). Commentary on the Old Testament. Peabody, MA: Hendrickson, Vol 9, 98-101.
Neusner, J. (2011). The Babylonian Talmud: A Translation and Commentary. Peabody, MA: Hendrickson Publishers, Vol 19, 190-191.