The cool factor- who has it?

Miles Davis and whoever is #2 is not even close. Miles was cool before being cool was cool. One might assume that anyone who can play a horn should be able to sing as well. Chet Baker disproves that assumption.

Dylan

Jagger and Richards for sure....and Charlie.

Garcia

Tom Waits

Chan Marshall (Cat Power)

Patti Smith

Johnny Cash

Willie Nelson...I think?

Duane Allman

Zappa was kinda cool

Chuck Berry

Grace Slick

I didn't include any jazz or blues musicians because they're almost all cool.

@woofhaven1992 ...but glad you did....👍😎 +10er...
Saw R.L.Jones in Berkley...  Was great until some Dhead in the front row handed  her a half a bottle of J. Daniels'....
Couple of numbers, she really carried the mood well....later, slid into slightly sloppy.

Stopped touring not long after....
Caught the mood, but the mood caught her...

@foggyus91 yeah, not really a debate on vocal chops... if that were the case Joe Strummer & Mick Jones would be in right the mix of your "Tiny Tim" analogy lol. Point is, I think we both find Chet Baker super cool, in spite of his limited vocal abilities, as was asked by the OP 

Mark Knoffler