I don't know for sure but according to kotobank.jp it's an onomatopoeia for air leaking through your mouth or nose. Given the context it seems fair to assume that if the goat parts its lips but keeps its teeth together and then tries breathing out through its mouth then it'll make a faint whistling noise as the air is coming out of the gap where it once had a tooth.

ふが　ふが - Parecen dos bicicletas; un poco de humor, saludos