When a chicken sits in a boat its animation is always falling. It doesn't stop until the boat is broken.
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Can confirm in 21w13a.
Video attached.
Can confirm in 21w14a.
Can confirm in 21w15a.
Can confirm in 21w16a.
Can confirm in 1.17.
Can confirm in 1.17.1.

Spawning any mob with a chicken as passenger will also make the chicken have flapping animation too

Can confirm in 1.20-pre5

In 24w37a
Can confirm. Also affects 21w11a.