Bereishis 7:21 implies the birds died first in the Mabul:
וַיִּגְוַע כָּל־בָּשָׂר הָרֹמֵשׂ עַל־הָאָרֶץ בָּעוֹף וּבַבְּהֵמָה וּבַחַיָּה וּבְכָל־הַשֶּׁרֶץ הַשֹּׁרֵץ עַל־הָאָרֶץ וְכֹל הָאָדָם׃ - And all flesh that stirred on earth perished — birds, cattle, beasts, and all the things that swarmed upon the earth, and all humankind.
However, two pesukim later (7:23) implies the birds died last:
וַיִּמַח אֶת־כָּל־הַיְקוּם אֲשֶׁר עַל־פְּנֵי הָאֲדָמָה מֵאָדָם עַד־בְּהֵמָה עַד־רֶמֶשׂ וְעַד־עוֹף הַשָּׁמַיִם וַיִּמָּחוּ מִן־הָאָרֶץ וַיִשָּׁאֶר אַךְ־נֹחַ וַאֲשֶׁר אִתּוֹ בַּתֵּבָה׃ - All existence on earth was blotted out—humans, cattle, creeping things, and birds of the sky; they were blotted out from the earth. Only Noah was left, and those with him in the ark.
Although maybe the birds were struck first by the heavy rainfall, they also could have flown to the highest available points then hovered for longer - when did they die in the flood?