This doesn't sound hugely fun for Kenshiro though not completely unfeasible. If Gilgamesh can pull out any of his significant techniques then Kenshiro likely isn't going to take it.
Hmm... he doesn't actually have to reach him, Kenshiro does have long range attacks in the Hokuto Goshou-ha and Tenha Kassatsu - both of which are effectively laser beams which make people explode. He can also use Nanto Seiken cutting techniques from range as well.
He's also
veeeeery quick, as outlined here in my speed breakdown post. I'd put him in the like... triple-ish digits of mach or something in that area. Hokuto no Ken is sometimes a little weird and esoteric in its speed presentations.
How durable is Gilgamesh anyhow? Ken could perhaps fire a chi blast and then close distance?