Many of the resources I've encountered say that Flack means "Dweller in a field of flagstones"... regardless of the origin given, the definition is always the same. It's very perplexing to say the least.
The Flack surname probably originated in the British Isles... this is based on two facts... most people with the surname live in countries that were once part of the British Empire, and most immigrants with this surname seem to have imigrated from either Scotland, England, or Ireland. Many others, in far fewer numbers, have come from every country in Europe. Unfortunately, without written evidence of an origin, its very hard to prove where Flack came from.
I do know that Flack is one of the least common surnames in the world... all the more reason to cherish it. A little over 8,000 live in the United States... according to the Social Security index.