What type of embouchure I need to get more of a jazzier sound on alto sax?

I have been playing alto sax for 3 yrs and I cant get rid of my stupid
thin tone.

I am sick of my tone, I want to get a jazzier tone. I want to sound
like Peter King on alto sax.
What are some things I can do to change my embouchure?
I dont roll my lips when I play sax.
Any techniques?
I feel like I sound terrible when I do vibrato.
How do professionals do it so perfectly? Is it with their jaw,
diaphragm, or their lip?
Im starting to hate my tone.