Obviously, they're meant to be reptiles. But I'm a nerd and I think these things through too much. I mean, c'mon. I have a lot of theories to make sense of it. SO here goes nothing.
There will be talk of mammaries in this article.
1. They're actually warm-blooded.
A lot of kritters and maybe a single krusha hop/strut around in the icy peaks of Gorilla Glacier, in the first game. The second game had krunchas walking about merrily in K. Rool's own personal ice storage. And let's not forget the skiddas around the K3! A reptile wouldn't last in those icy areas for more than an hour.
Not to mention they run around for little reason nearly all the time. Real crocodiles lay about in the sun all day, only moving to eat or mate, being dependent on warmth to survive. Kremlings usually also spend time playing video games and running after crystal coconuts, among other frivolous pastimes.
That, and King K. Rool clearly blushes in shame, in the episode Just Kidding.
2. The females are life-bearing
Before birth, all mammals are connected with their mom by an umbilical cord. This thing comes straight from their belly and when the baby gets born, the cord is cut off/bitten off/left until it falls off on its own. Usually, a scar, most often referred to as the navel or belly button, remains.
Did you know I used to have a strange, untold fear of navels? I kind of got over it.
Alas, that aside, some Kremlings clearly have 'em too. Of course, K. Rool comes to mind, but then, his golden stomach is merely an armour.
Certain enemies, though...
Mostly the Klumps (the enemies, not the individual.) and Kannons. What does this mean? They don't get hatched from eggs. The females are life-bearing.
3. They have boobs!
Traits only present with mammals. It's all in the name; mammaries. And yet Rare manages to take it too far. Sure, comic relief... but I mean, just look at Klump.
I said; 'Look at Klump'. Not 'look at his appallingly large and in-your-face moobs.', even though that was the point. Now look what you've done.
Bad example, but tits are tits. Sorry for that. Again, that's only present with mammals. Reptiles don't need 'em 'cuz their young hatch from eggs and are self-dependent very quickly.
We also have Kalypso, the first female Kremling in about ten years, and she ain't exactly flat-chested either. So it can be assumed that in a manner similar to mammals, Kremlings nurse their young in the same way humans do.
The conclusion? Kremlings aren't reptiles, but instead, they're more closely related to mammals... but even so they're probably something different altogether.