This is a mash up of “fly in the ointment” and “flaw in the logic”, both referring to a drawback. Confusion may also be caused by the similar sounding words “fly” and “flaw”. Thanks to Barry Eigen for passing this gem along!
I heard this one at a meeting. My guess is that the speaker was thinking of the phrases “swimming against the current” (go against prevailing thought or opinion) and “off to a flying start” (good beginning), both indicating movement. He may also have been thinking of the difficulty flying through wind currents. Then again, as in many blended idiom mix-ups, the speaker probably forgot or did not know the accepted idiom.