In Old/Middle English, the prefix "a-" meant "on", "in", or "engaged in". (It's the first element in e.g. "asleep".)
It's still a living prefix, in conjunction with an ING form; usually, it has a jocular or deliberately old-fashioned air.
So in your example, it means "time is (engaged in) flying".
Perhaps Tagore (I think it's a "he", by the way) was also thinking of the poem by Herrick that begins:
Gather ye rosebuds while ye may,
Old Time is still a-flying,
And this same flower that smiles today
Tomorrow will be dying.
Have a good evening,