Video plays too fast in flash browser plugin and some of the video players but not VLC.

Installation is fresh new except that Nvidia driver is installed.

How to make video play with normal speed?

if you are not going to include a link so we can check it .....
nor
if you do not bother to inform us as to WHAT browser you are using ...
Then there is not much we can do

nor
if you are not going to inform us as to WHAT version this unknown browser is ......
( for all we know it is a antique firefox3 )

Is the flash plugin updated ?

well, op did mention a frsh install of debian, which would suggest a fairly new version of iceweasel.

but generally john vv is right. we need much more information about your general setup (it seems you already recognize which parts could be responsible).

one simple step for troubleshooting is: open your browser from a terminal window, try to reproduce the problem and see if you get relevant messages.

btw, if the problem is indeed flash-related there's not much we, or in fact any linux user, can do, because flash is closed source.

With so little information, it's hard to tell what exactly the problem is, but I once had a similar issue under an earlier Ubuntu setup. Turned out it had something to do with some audio driver; I don't remember the details, but I think it was some kind of digital audio module that got loaded, and that, IIRC, I had to blacklist in order to solve the problem; something like "intel_hda" was the culprit, I believe.

Somewhere on the net there must still be some traces about this issue, and what I did to resolve it (I think I found the solution when I browsed through some Chrome forum or some such, and I posted my solution there--even though I had the problem under Firefox).

I beleive it is not browser related: chromium and firefox has the problem.
But i also beleive it is not flash related because Totem has the problem too.

Flash is updated to last Linux version: Shockwave Flash 11.2 r202
Iceweasel 38.3.0
Chromium Version 46.0.2490.71 Built on 8.2, running on Debian 8.2 (64-bit)

Looked it up for you. The issue as I encountered it was reported under Chromium, but wasn't specific to it.
Here's my comment on what I did to resolve it: Chromium Issue 108396: HTML5 audio and video has glitchy sound on Linux with PulseAudio.
Obviously, I cannot be sure that your problem is identical to this issue, but perhaps it offers you a few pointers.

Run Totem in terminal and see what it tells you maybe.

Ok. I updated to 4.2 kernel from backports and updated my nvidia drivers to 355 with patch from nvidia forums for compilation with 4.2 dependency.

Problem disappeared. Also i add additional information on problem here:

glxgears behaves strangely showing exactly 60 FPS like VSYNC beeing enabled but "Sync to VBlank" is still unchecked in nvidia configuration.

Before that glxgears were showing 18000 FPS without explicitly specifying vblank_mode=0:

vblank_mode=0 glxgears