Two yellow spots on its wings.
This would give me the idea that there might be two spots on each wing.
A yellow spot on both wings.
I think this is correct, and it does make clear that there is one spot on each wing.
The main thing is, when we are talking about birds, we know they generally have two wings. You might even describe it as:
A yellow spot on the wing.
And people would assume (as birds tend to have identical, if mirrored) wings, that this goes for all wings the bird possesses.
Another option, and I think the most readable, would be
A yellow spot on each wing.
I would avoid mentioning the total number of spots, as you will risk confusing people: does two spots mean two spots per wing or two spots per two wings.