LEDs don't flicker, at least like electronboy described, if driven with a decent DC source.
However, there may be some types of
noise that manifest themselves in some types of use (I'm thinking e.g. of flicker (1/f) noise or shot noise). My intuition would be worried about
shot noise. While it's a Poisson process because it's caused by discrete events, I believe the power spectrum is similar to that of Johnson noise. I have an old friend who's an optical engineer and I can ping him on your behalf if needed. You're also going to have to detect the photons and that will lead to shot noise too. If you can determine you have significant Johnson noise in your detector, consider using a thermoelectric device to cool the detector (detector cooling is often done in particle and photon detectors). I can't help much further, as I took my nuclear physics class before those guys landed on the moon...
Since you want to use the LED source in an interferometer, you're going to be integrating the signal over some spatial distance and I'd imagine something like shot noise would somewhat average out since it won't be spatially coherent. This shouldn't be too hard to check with e.g. a cheap red LED.
From the few UV LEDs I've measured, the FWHM is typically around 5-10 nm; the same is true for LEDs in the visible region. I've attached a graph of one spectrum I made about 5 years ago. I had some UV LEDs that had center frequencies of 350 and 365 nm (the mercury line), but I don't know where they are, so I can't measure them. I remember they were in a mailing envelope, so lemme look for them tomorrow. Alas, I think I tossed them out when I moved from the other room...
Edit: on second thought, that statement about the noise averaging out may be kinda dumb. All those noise pulses add up and you won't be able to ignore them. But the spatial part of the comment is probably OK -- it just means that because of the finite size of your detector, you'll probably see fewer spikes; they'll average out to a continuous noise signal. Or, all of this could be highly diluted eyewash...