The Q are omnipotent (according to them saying so many times in the course of Deja Q). But I don't recall ever seeing a Q transport without making that 'flash'. Do we ever see a Q transport without making a flash and, if not, does this mean that they're actually NOT omnipotent. (Note: I'm ignoring what Quinn says in VOY).
The 'flash' and the transitional noise appears to be the default position (we see various Q and Q-like beings creating it) whereas a transition without a flash would seem to take some conscious effort of will.
Q also makes the Calamarain disappear (in TNG : "Deja Q") without any flash.
He blows on the palm of his hand. The glow is blown away. Q2 reacts, nods okay.
No, we never see him doing that. What makes me so certain is the fact, that the special effect we are looking for is, that the camera points at an empty spot, then, one frame later there is Q standing there. This "special effect" just looks silly - I know, because I used it as transporter-effect when I got my first camcorder. I don't remember seeing something that stupid at Star Trek.
We sometimes see Q suddenly entering the screen where he isn't supposed to be - without a flash, suddenly being in a room we, did not see him entering by conventional means (i.e. the door). But we don't know how he got there since it happened off-screen. It could be with- or without the flash.
But even if he needed the flash: Theologists had always had a hard time with omnipotence: Can Q make a Hasperat so strong that he could not eat it? So they came up with the solution, that omnipotence does not extend to doing logically impossible things. It might be, that for reasons we don't know yet, it is logically impossible for a Q to appear somewhere without the flash. In that case he could still be omnipotent while being unable to appear without a flash.
[Pure speculation: Quinn might refer to the fact that omnipotence is vastly overrated, because the boundaries of logical possibility are annoyingly tight for a beeing that is otherwise capable of doing everything]