What is the cooldown time for feeding berries to ally Pokémon?
As indicated in the question How many berries can I feed to a Pokémon?, I am aware that after feeding 10 berries to an ally Pokémon, it becomes "full".
How long do I have to wait before the Pokémon becomes "hungry" again so that I can feed it more berries?
A Silph Road Reddit post indicates a 30 minute fixed timer. The timer starts on the first berry and resets after 30 minutes. That is, if you feed 5 berries, wait 15 minutes, feed 5 berries, wait 15 minutes, the timer resets and you may feed 10 berries immediately.
There is another restriction on feeding up to 10 pokemon within a 30 minute rolling window.