The effect of the warlock's Misty Escape feature is that when the warlock takes damage she can use her reaction to teleport away to a location of her choosing within range.
The effect of failing a saving throw against the dissonant whispers spell is that the target must use her reaction if available to move up to her speed away from the caster.
Suppose a warlock with the Misty Escape feature fails her save against dissonant whispers. If she has her reaction available, whichever effect happens first will use that reaction, and the second effect will not happen because her reaction has already been used. So, which effect happens?
Best Answer
Dissonant Whispers happens.
With Misty Escape, the warlock "can" use their reaction to teleport away, but when failing a save against dissonant whispers the warlock "must immediately" use their reaction to flee.
In D&D specific beats general, and "must" is more specific than "can" because "must" is compulsory while "can" is optional.
So, the effect of dissonant whispers happens first, preventing the effect of Misty Escape.