The "flashing" process is essentially instantaneous, but not literally so.
Some qualitative musings follow:
Depending upon the pressure drop, there could be some small fraction of a second elapsed for some of the liquid to boil off to vapor at the lower pressure. (We look at thermodynamics as if we're at equilibrium conditions, and it often isn't so, but to no great error.) The mass fraction that flashes will typically be small, and in a typical industrial environment, with lots of rough surfaces at which boiling will initiate (nucleation sites), it will be very fast. The temperature drop is in a sense due to "evaporative cooling", so there could actually be a non-uniformity of the temperature immediately after the throttling.
If you are throttling over a very large pressure drop, and the mass fraction going to vapor is mor than 5 or 10 percent, then it is possible that this really would take some time (i.e. pipe length) to complete itself, but that is only a guess. Someone with similar experience, or someone who is expert at non-equilibrium thermodynamics will have to tell you better.
For practical purposes, it strikes me as something I wouldn't concern myself with in any case.
What are your concerns?