"The children want more buns."
Translation:Barnen vill ha fler bullar.
No, that doesn't work. It sounds cut off and I wouldn't understand whether you had left out the number or left out the name of the person you wanted to give them to (Something like Jag vill ha bullar till mormor 'I want buns for grandma' could well be my first guess). So it would be both ungrammatical and hard to guess its meaning.
I assume that you don't know exactly how many more buns the children want (only that they want more than they have now). So why the default "fler" here? "mer" is counted correct, but I assumed it would be the most logic one here.
Is there a reason "fler" is the one to go for here?
fler is for countable nouns regardless of whether you actually count them or not. But as you noticed, the amount can also be treated as an indefinite substance, in which case mer works as well. The latter is often considered colloquial, and mostly not suitable for formal text, but perfectly fine to use in ordinary speech.
Tack! I probably have heard https://www.musixmatch.com/lyrics/Astrid-Lindgren/Ge-mig-mera-köttbullar too often and am used to "mer" :)