Rambis has coached under Phil Jackson, Mike D'Antoni and Del Harris. He's not a newbie. I think any head coach would be fine with having him on the roster so long as he was secure about his job. If it's someone who is just starting his coaching career, I don't think they'd feel comfortable with Kurt. If it's someone established like Thibodeau, I don't see that as a problem. He was on D'Antoni's coaching roster in 2013-14, I read it on his Wikipedia page.
Phil should definitely consider a Thibodeau/Rambis pairing, but I'm still holding out hope that Jackson is willing to coach himself if Rambis is staying on. I can't see a situation where Phil Jackson can present a better sales pitch to free agents than with him as coach and in terms of a coach who understands the way to insert the Triangle offense to utilize as an asset to the team, it doesn't get better than Phil.
I like Thibs a ton, not sure how he would mesh with Melo, Dolan and Phil. That's many different personalities there. Thibs is a straight forward guy, who demands his team play a high level of defense. He would have a strategic approach that is quite different from Phil's, and he's already have been rumored to not have a good relationship with Dolan. I don't see it happening.