YES, there are several Hebrew phrases repeated between Genesis 1 and the various chapters in the Flood narrative, so much so that I think the Flood narrative is consciously referencing Genesis 1.
The first parallel is actually an anti-parallel; everything God creates in Genesis 1 is "טוֹב" (good) and the people on earth in Genesis 6 are "רעע/רעה" (evil).
Also, as Dottard stated, you have a lot of parallels in thematic material between the two stories, including the same set of events in reverse.
But there are some specific parallels in language which go a bit beyond thematic parallels or the parallels you highlight in your question. Here are the most important ones to me:
"וַיֹּ֣אמֶר יְהוָ֗ה אֶמְחֶ֨ה אֶת־הָאָדָ֤ם אֲשֶׁר־בָּרָ֙אתִי֙ מֵעַל֙ פְּנֵ֣י הָֽאֲדָמָ֔ה מֵֽאָדָם֙ עַד־בְּהֵמָ֔ה עַד־רֶ֖מֶשׂ וְעַד־ע֣וֹף הַשָּׁמָ֑יִם כִּ֥י נִחַ֖מְתִּי כִּ֥י עֲשִׂיתִֽם" (Genesis 6:7)
'So the Lord said, “I will wipe from the face of the earth the human race I have created—and with them the animals, the birds and the creatures that move along the ground—for I regret that I have made them.”' (NIV)
There are specific Hebrew words for animals in this verse: First, "בהםה" ("Beast," "cattle," or "livestock"), second, "רםשׂ" ("creeping thing"), third, "עוֹף השּׁמים" ("birds of the air"), and fourth, "אדם" ("man," as in "human being," not an animal. Also the name of Adam). These are the word used to describe the creation of humans and animals in Genesis 1. All of these words, for instance, appear in Genesis 1:26 when Adam/humanity is given dominion over this exact set of animals (plus the fish of the sea, which obviously aren't going to be destroyed by a flood):
"וַיֹּ֣אמֶר אֱלֹהִ֔ים נַֽעֲשֶׂ֥ה אָדָ֛ם בְּצַלְמֵ֖נוּ כִּדְמוּתֵ֑נוּ וְיִרְדּוּ֩ בִדְגַ֨ת הַיָּ֜ם וּבְע֣וֹף הַשָּׁמַ֗יִם וּבַבְּהֵמָה֙ וּבְכָל־הָאָ֔רֶץ וּבְכָל־הָרֶ֖מֶשׂ הָֽרֹמֵ֥שׂ עַל־הָאָֽרֶץ"
'Then God said, “Let us make mankind in our image, in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground.”' (Genesis 1:26, Hebrew/NIV)
"בהםה" additionally appears in Genesis 1:24-25 along with "רםשׂ", you get "עוֹף" in Genesis 1:20-22, and of course "אדם" in Genesis 1:26. These all occur again in Genesis 1:30 along with another significant Hebrew parallel, the "breath of life" ("נפשׁ חיה"/"רוּח חיים"). See here for a better description of this as it applies to these passages, but tl;dr the two phrases, the first of which occurs in Genesis 6 and the second in Genesis 1, are synonyms which both mean "breath of life".
I think the "Spirit of God hovering over the waters" ("וְר֣וּחַ אֱלֹהִ֔ים מְרַחֶ֖פֶת עַל־פְּנֵ֥י הַמָּֽיִם") in Genesis 1:2 is best paralleled by Genesis 8:1: "God... sent a wind over the earth, and the waters receded." ("וַיַּעֲבֵ֨ר אֱלֹהִ֥ים ר֙וּחַ֙ עַל־הָאָ֔רֶץ וַיָּשֹׁ֖כּוּ הַמָּֽיִם") The word "רוּחַ" used in both these verse can be translated "breath", "wind," or "spirit."
Finally, God commands every animal that survives the flood to "be fruitful and multiply" ("וּפָר֥וּ וְרָב֖וּ עַל־הָאָֽרֶץ"), Genesis 8:17, echoing the same language in Genesis 1:28 ("פְּר֥וּ וּרְב֛וּ וּמִלְא֥וּ אֶת־הָאָ֖רֶץ") "Be fruitful, and multiply, and replenish the earth."