First of all, Donkey calls himself color blind. We can assume that he is an expert on the topic, so we have to take his word for it.
The term "color blind" implies that Donkey's vision is somehow deficient from normal members of his species. If so, and he does have some kind of sight problem, then we have no way of knowing how well other donkeys in the fairy-tale world can see.
However, Donkey's inability to find a "blue flower with red thorns" lines up perfectly with how real-world donkeys can see. Donkeys, like all equines, are naturally dichromatic - they only have two-color vision, as opposed to human three-color vision.
Specifically, real-world donkeys have no red color vision -- there's no cell in their eye that is triggered off of specifically red colors. To such an animal, red would merely look like a shade of blue-green somewhere. If a human had this vision, we would called them red-green color-blind.
Thus, Donkey's inability to locate a flower that had "red thorns" very strongly implies that, in human terms, he is effectively color-blind.