I think the best suit would be to go with would be similar to the suit in the spiderman movies or the suits the tributes wore in Catching Fire of the Hunger Games series. A textured/pattern form fitting suit that had painted muscle shading and stitching in the right areas like Raimi's spiderman suits, MOS superman's suit and Thor's arms when covered in the armor (if you look closely you can see his arms biceps and triceps were shaded to accentuate his already toned physique) would look great.
You don't need a purely spandex runner suit or a rubber or leather suit. I think Ender's Game, XMEN DOFP, Hunger Game's, MOS, and Spiderman all did a great job with textured form-fitting, somewhat spandex, suits that used a combination of different materials, multiple patterns, clever stitching, muscle padding and shading. That's what Flash needs to wear.
As for the cowl this seems to be the trickiest part. I think they should use a combination of either a thicker material, possibly leather, for the head that way they can get the brow detail and facial features to show, but use a thinner material so that he can turn his neck. The problem with comic character cowls is they always want to use a thick material like leather or rubber to simulate neck and throat lines and make the neck and traps look muscular and larger to show definition. I don't think this is always necessary. However if they do do that then they should cut the neck from the head cowl but cover it with thin fabric or join the pieces with a stretch material that way it all looks one piece, but allows the wearer to turn his head full range.
I still can't figure out why these costume designers haven't done this yet. I haven't liked any of Batman's cowls or Flash's cowls and it is relatively an easy thing to do. And before anyone says "oh who are you to criticize these professionals and how many suits have you built blah blah blah" I have looked into it and it is very possible to make a comic cowl in real life that isn't made entirely of rubber, latex or leather.