Owlins and Unarmored Movement

So I haven’t been able to find anything online about this possible ‘exploit’. Owlins get a flying speed equal to their walking speed as long as they’re not in medium or heavy armor. Monk’s Unarmored Movement notoriously increases all of a creature’s speeds. So my question is: wouldn’t it technically be doubled for an owlin’s fly speed (walk speed would be increased which automatically increases fly speed but then fly speed would also be increased), or does the ‘equal to your walking speed’ override this?