I do not know. I have never fed my sylestis once and i dont know how to get the food. I`ve heard theres a "restock food" button in stables? idk where it is :'/

There is no actual food. In the stable on the top right you will see four blue buttons. The top left blue button says 'feed pets'. Click that. From there a new pop up will appear asking if you want to feed just your current stable, or all stables (assuming you have more than one), and will show you how many hungry pets you have and the price to feed them. Click whichever option you need (current/all stabled), and the gold to buy the food and feed the pets will be deducted. And that's it! You've fed your pets ^.^

edit to add:
If you want to feed just certain pets, for some reason, you can click on the pet's profile and at the bottom of the 'information' box, there will be a button that says 'Feed Sylesti'. Click that, and, again, the gold required to feed the pet will be deducted from your account and your pet will be fed!

k, thnx!