Even if you hold him back, you do NOT know, if that will "cure" him of his complaining.
A little child like that, cannot "decide" if he should stay in Kindergarten or not. They do not understand the intellectual bigger picture of it.
I know many kids who repeated Kinder.
They are fine.
Kids didn't make fun of them.
The child was fine about it. And because, the parents explained the positives about it. Not making it like a big deal or that something is "wrong" with their child.
Your child is academically on par. If he repeats Kinder, than what? What will he learn academically? Or be bored?
There are some kids that are always just complainers or "immature."
So then what? Should they keep repeating Kinder until they are too old or too big in height?
Does your child get enough sleep? Maybe at school he is tired and over tired, hence he complains. At school. When a kid is overtired or not getting enough sleep and are "working" hard in school, they falter. They don't have the stamina to keep on task or to do what is expected of them. And they don't have much patience or tolerance for things going on in class.
So if your child is tired or not getting enough sleep, and it is affecting his behavior at school, being he is 5... then he needs more sleep. And/or an earlier bedtime.
And your child, doesn't like changes in routines. Well many kids are that way too. But they learn. Its life. Its school.
Then, there is a boy in my daughter's grade level, (4th grade), that has been that way (like your son), since Kindergarten. He is on par academically and has not been held back. But... he is always complaining or belly aching about something, and all the other kids and Teachers know he is like that. He just doesn't want to be responsible for his actions. Even if he was held back in Kindergarten, he would still be that way. In school.