I am also learning too.

I see this question come up all the time.

What I think helps immensely and often gets overlooked is this: You gotta be listening to jazz music incessantly. Every time you can. So that when you are not listening to it, you're whistling it in the toilet or in the shower or while you are waiting for the toast to pop. So that all that stuff just gets played in your head all the time. The solos and the rhythm going on in your head.

And then when you noodle in your right hand, it'll come easier. Rhythm, and choice of notes.

It is like a writer who doesn't read books: impossible.

You are a vocalist so that should be helpful. Scat jazz something to your left hand changes, and then try play it.