1.) Make sure the pet you want to feed is summoned.
2.) Make sure food is in your inventory instead of vault, if it's not already.
3.) Reload the page if it still does it. ^^
4.) If problem still persist then try clearing both flash AND browser cache, browser cookies and etc.
5.) Try a different browser if that doesn't work (Firefox, waterfox, cometbird, chrome, internet explorer, opera, safari, etc..)
6.) Use contact us
to send a ticket and explain what you did already (link to this post if you want). They should be able to help you. :3
Hope this helps.