Feeding a flower to a brown mooshroom does not perform hand animation

From the way you have described it, this is intentional. A flower does nothing to a mooshroom. If you mean the flower mushroom from Minecraft Earth, please go to feedback.minecraft.net if you want to submit a suggestion for the Mooblooms to be added into the normal game.

I am stunned and amazed at the fact that I have never seen a brown mooshroom before. Confirmed in both 1.15.2 and 20w18a.

Please do not report the same issue multiple times.