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.
We can say anything. We can propose our "taste" as truth...
But facts spoke themselves sometimes :
I pick and past it from google :
«Chet Baker’s first vocal album, Chet Baker Sings, released in 1954, was a significant success that propelled him to stardom as both a trumpeter and vocalist. The album, featuring his interpretations of popular standards, was a hit with audiences and critics, and helped establish him as a prominent figure in the West Coast cool jazz scene »
Then Say it in this way : Chet Baker sings crappy and it is my opinion...
And i will say it my way and i am not alone saying it : "the Prince of cool" was Baker because he sing as he play : cool with no bravado...