So apparently the Blue Rim is a crossing between a blue betta and a dragon betta, in a way such that the base colour is blue but the dragon mantle exceeds into the fins and causes the rims.
So this means crossing a blue with a blue rim will yield several interesting results.
One result could be a full blue betta, since both bettas have a base colour of blue.
Another is a blue dragon betta, which is really cool, but rather rare it seems
Of course you could have some blue rims.
You could also achieve a somewhat marbled pattern, as sometimes the dragon mantle don't cover the betta evenly.
Full white or 'Milky white' where the mantle spreads fully to the entire fins.
Of course this is vry broad, and realistically due to so many alleles in bettas controlling colour, scale pattern and fin shape, you'll probably get a skittles selection of bettas