English Translation
Eat what you are served; no buts about it.
This is spoken as I S S rather than iss…
Would Germans use “bekommen” here? I’m unsure.
I myself would say:
“Iss, was dir serviert wird.”
Now you at least have an alternative to choose. 
I’d personally also prefer “ohne Aber” rather than “keine Aber” or “kein Aber”. It simply sounds more natural to me, but “kein” also works, I think.
German has the idiom “ohne Wenn und Aber”, but I don’t know whether that’s the best option here. I’m unsure if a child who doesn’t want to eat its cauliflower would negotiate with its parents, “I’ll eat my greens, but only if I may play Nintendo for 30 more minutes.” (I don’t have children though. 
) Whereas “Ich will aber nicht.” will surely be said.
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I don’t quite agree with the “ohne Wenn und Aber”. This means “ohne Bedenken”, i.e. “no doubts, no reservations, 100% agree”.
But this is not what the situation calls for. Here, “no buts” means “no complaining, no talking back, no whining or moaning, end of discussion”.
So for a german translation, I’d suggest “kein Aber” (singular! plural is just weird and looks like a literal translation from english), “keine Widerrede” (“no backtalk”), or maybe even “basta!” or “Ende der Diskussion”.
Also, “serviert bekommen” sounds fine to me. It’s an idiomatic use of “bekommen”. “was dir serviert wird” works too, of course, but sounds a little more formal, and I don’t see that parent-to-child talk needs to be formal.
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You’re right, I revised my answer.