Who's the best. Mmmm...Tough and IMO very subjective. Also, IMHO, some of the best players don't or can't teach their skills....teaching is very different from playing.

I'm a recently converted (approx. 1 yr.) OMB jazz/ big band trumpet player and have studied (trumpet performance/jazz-degree) and played improv for decades. My current OMB gigs are about 95% instrumental with improv as my 'thing'. I'm working on adding more vocals into my repertoire to open my market.

I'm still learning to operate the arranger/workstation and don't consider myself an expert on this instrument and certainly NOT "The Best".

I don't know where you are but at the risk of being obvious; improv, as I learned & implement, requires a complete mastery of ALL 12 Major & 12 Harmonic minor scales at a minimum. Hopefully @ 200 BPM & flawless. This is the starting point, just the starting point, as I was taught. A basic understanding of seeing and recognizing II, V7, I, - II, V, etc. progressions is also a must IMO. Those are progressions that the root major scale will be your basic 'beginning' for improv.

There are some methods, Jamey Aebersold, etc., that a lot of schools use to help teach improv. I know of jazz professors that teach on-line using Skype, YouTube, and just email with attached audio &/or video attachments.

I've had people ask me over the years but it usually ends when the amount of preparation and commitment wains. Adults are especially difficult to teach because their 'lives' get in the way of the commitment to practice scales. There is an advantage and exception to mastery of all scales on the arrgr/wkstn if you use the transpose option of your keyboard. I have trouble with that because of my years of playing in the key, maybe a handicap with today's technology.

This is all just my experience and opinion! Please be kind, there are other opinions!!

Drop me a PM or email if you want. Considering I'm a relative newbie to this forum you might as well ignore me anyway.