If the overlay is only seen when they are eating, I'd just create it in the eating proc, and then flick() its state (heck, you could just give it one icon_state that is what you want it to show, and when it is created, it will just show that animation)

Eat()
var/obj/eat_overlay/E = new()
src.overlays += E
flick("FoodLeat", E)
del(E)

Or something along those lines... But like I mentioned, if you just give it the one icon_state that shows what you want to display, then there's no need for flick()... But if you do it this way, you'll have to add in a sleep() delay before it is deleted to give it enough time to be seen...

Another method I think would work (and would be much more flexible) would be as follows:

mob
var/obj/effect_overlay/effect_overlay

Login()
var/obj/effect_overlay/E = new()
src.overlays += E
src.effect_overlay = E

verb
Eat()
flick("eat",src.effect_overlay)
Explode()
flick("explode",src.effect_overlay)

obj
effect_overlay
icon = 'effects.dmi'

This way, you can add one overlay object with all of the effects you need, set a mob var to point to that object, and use that var to flick() that particular overlay object to whatever effect you want it to show...