They do get some inborn skills with 100 BLUP...

Yes, ideally you want to get your donkeys to 100 blup which is really difficult, so usually people stop at 60 blup (training/rides done, without 20 wins).

You don't want to increase their GP like regular horses, it's the opposite! It sounds really counter-intuitive and a lot of people don't bother, or maybe don't understand because it's so different from how every other species works in this game - but you want the lowest GP possible. If you don't blup your donkeys, they lose less GP each time you breed.

If you look on the best teams page, you will see the number one team under genetic potential has the lowest GP (231 compared to 2nd place team at 306).

Of course, you don't have to do any of that, you can just have fun, but since donkeys can ordinarily only breed 3 times in their lifespan, it's worth making them the best (or worst) you can.