I'd say this version of the a- prefix (a-flying, a-hunting, etc.) is the same as aglow, for example, where it means in the process of, in a particular state. I wouldn't call it a circumfix at all - it's just that in those first two words there's also a suffix -ing (again, indicating a continuous state).
I think there are at least a dozen different a- prefixes in English, but this particular one seems to me to be either the same or closely related to the one in aside, aback, etc., where it means to, towards. etymonline(1) says...
a- (1) in native (derived from O.E.) words, most commonly represents O.E. an "on" (see a (2)), as in alive, asleep, abroad, afoot, etc., forming adjectives and adverbs from nouns; but it also can be M.E. of, as in anew, abreast (1590s); or a reduced form of O.E. pp. prefix ge-, as in aware; or the O.E. intens. a-, as in arise, awake, ashame, marking a verb as momentary, a single event.
a- (2) prefix meaning "not," from L. a-, short for ab "away from" (cf. avert), or its cognate, Gk. a-, short for apo "away from, from," both cognate with Skt. apa "away from," Goth. af, O.E. of.
EDIT: The question of what exactly constitutes a "circumfix" in English is tricky, to say the least. I used to think y---t in now-archaic yclept (from also-archaic clepe "to name, call, dub, entitle") was about the only example. But here are guys in Wikipedia 'talk' arguing for em---en (embolden), and be---ed (beloved). So maybe a---ing qualifies after all.