I can't say I've heard it used about the sky.. Most often it's usen when talking about sound, "a muffled scream" = a scream that's concealed/ softened by something, perhaps a pillow. A muffled trumpet. Or if you're concealing something else. If it's used as an adjective for the sky its meaning is probably derived from this. A "muffled" sky would be soft, grey and free of contours. If it's "muffling" then perhaps it's suggested that it works like a pillow on its surroundings, swallowing life and excitement.

Hailey, A "muffling" sky does not have to be any certain color or even have clouds. The word "muffling" is used by the writer as a mood setter. A muffling sky is dominant, stifling. There is something about the sky that is oppressive. In order to get a more exact meaning you would need to know how the "muffling sky" relates to the rest of the narrative and the characters in the narrative.

Nope - it's taken from an American book.

Sorry, I've also never heard of "muffling sky". Are you studying British English only?