All of these are acceptable as well as some
I'm sure I missed:
I ate enough burgers.
I have eaten enough burgers.
I have had enough burgers.
I've eaten plenty of burgers.
I don't want anymore.
I've had my fill of burgers.
ell.stackexchange.com/users/6277/meer2kat
Simpler to say: "I have eaten enough burgers today."
ell.stackexchange.com/users/5985/Gary's Student
I would say: "I have eaten my fill of burgers today."
ell.stackexchange.com/users/6525/Elian
As other people have indicated, there are several different ways this sort of thing can be said, but it's worth noting that some of them can have slightly different implications or impressions on the listener.
"I've had enough of (something)
" generally means that you've experienced so much of something that even thinking about it brings up bad feelings for you now.
For example: I've had enough of eating burgers.
I don't want to eat another one as long as I live!
On the other hand, saying something like "I've eaten enough burgers" or "I've had enough burgers" is a less strong statement, and might just mean that you're satisfied with the amount you've eaten and don't feel a need to eat more right now:
I've eaten enough burgers recently.
I think I'll have something else for dinner.
or I've had enough burgers today, but if you really want to go to the burger place, I suppose I could eat another one.
ell.stackexchange.com/users/6310/Foogod
Saying you already ate a food today is a common way of saying you don't want to eat any more.
I already ate burgers today.
People often use this construction with yesterday as well.
The meaning is the same, since the speaker ate burgers yesterday the listener knows they probably don't want any today either.
It is too soon to eat the same food again.
I had burgers yesterday.
The construction you used "I have had enough of eating burgers.
" is correct, but has a different meaning!
That sentnece means that you ate burgers so often (maybe every day for a year) and now you can't eat any more.
They don't taste good to you anymore.
ell.stackexchange.com/users/4301/Phil
I'd say I am fed up with burgers for today
ell.stackexchange.com/users/79638/Gio
I have had enough of eating burgers.   Can we say that if I eat too much burger continuosly through the day and don't want to eat it anymore?
I have had enough of eating burgers
ell.stackexchange.com
<grammar>
ell.stackexchange.com/questions/22968
ell.stackexchange.com/users/6314/user73963
Alternative ways to say this include: I already ate a burger today; I am fed up with burgers for today; I have eaten enough burgers today; or I have eaten my fill of burgers today. I have eaten enough/my fill, being fed up, saying you already ate something are all appropriate.
I have eaten enough/my fill, being fed up, saying you already ate something are all appropriate.