Do flergamarms exist?
Well, what do you mean by "flergamarms"? Or to put it more precisely, what empirical observations would you be able to make that would be different if flergamarms did exist than if they did not?
Flergamarms are invisible, intangible, and in fact, cannot be observed in any way. They have no observable effects, nor are they a logical consequence of something observable. As such, there is no such observation that would be different depending on the existence of flergamarms. So, do they exist?
Well, I wouldn't say they exist, but I'm also wouldn't say that they don't exist. Rather, I'd say that the question is meaningless. I would say that something can only have meaning if it's in some way connected to reality, and to be connected to reality, it has to be observable, or the logical consequence of something observable.
I'm not completely certain about that. Maybe there is some sense in which the term "flergamarm" is meaningful. I can't think of anything that could be though. And even if there is, there's still not much point in discussing such entities.