Googled this and there are some mentions of it being a game played by children in Nigeria. It’s even mentioned in Ben Okri’s The Famished Road.
However, there’s no explanation as to why shaking your hands might cause white spot to appear on the nails. Apparently, according to Don and those who have posted about it online, white spots do appear. Mere coincidence or is there a scientific explanation?
By the way, the white birds in question, the Leke Leke, are egrets, more specifically cattle egrets.