Thats a good question and as of what I have concluded from alot of research improving your flexibility may not "directly" effect your pace but by improving flexibility you may increase the length of your stride and strengthen the muscles in your legs.. if you picture your muscles like a rubber band and if you can pull a rubber band further then it can shoot further.., and running speed is the maximum amount of force that you can transfer into the ground with each step.

ex.-Kadour Ziani (world record vertical) streches for a minimum of 3 hours every day and can obviously push off of the ground with alot of force