I believe there is another slang-angle to the term--but maybe this was just a regional usage...?
Finger-flinging does have to do with difficult, knuckle-busting/virtuoso sleight-of-hand, but also with an element of showing off.
--Unlike poppin' wheelies on your bike, or burning rubber with your car, nobody in the audience is supposed to notice it at all.
A stud finger flinger, who may even have been able to use an easier method to accomplish the same end, will clench his jaw and whip-off a half-dozen invisible passes just because he can.
Thus, I suppose it is almost, extra-difficult sleight-of-hand for impressing magicians. The audience sees nothing, but we, knowing what is going on underneath, hear sqealing tires in the backs of our minds, as the maestro does metaphorical doughnuts in a parking lot for our benefit.
The times I have actually heard the term used in seriousness were always when someone or a groups of guys were really letting it fly. --Trying to top each other, or keeping a string of incredible happenings going--like a jam session.
It was usually one of the oldsters who would pull you over to a group of guys and say, "Boy the fingers are really flingin'!".
Thus, what that phrase means to me is looking over somebody's shoulder and watching Daryl, Derek Dingle, Michael Weber do stuff with a deck of cards that makes you want to weep tears of glee.
...I have only seen finger-flinging on rare occasions, and it had nothing to do with any tell-tale flutters, it was when some amazing [censored] was going down!
Of course, we also use the term because it is aliterary and dorky like bees knees or hostess w/the mostess--because we all wish we were hip, and around it the 20s and 30s... ;)