You can't play jazz on a theremin. There are a number of musical idioms that the theremin just doesn't fit into: Rock & Roll, Country and Jazz are perhaps three of the most obvious. I've seen people play the didgeridoo and the kazoo with a jazz combo and it works for a couple of minutes as a novelty effect but, like the theremin, they are unlikely to be a big hit on Bourbon Street.
In the jazz I have heard that includes a theremin, the thereminist has played in the traditional way while the other instruments supply the jazz feel. Sure, you can do a jazz rendition of OVER THE RAINBOW - hell, you can do a jazz rendition of O, HOLY NIGHT - but the theremin is a one-trick pony and regardless of whether it is playing with a jazz trio or the Boston Pops, it's going to do pretty much the same thing because it really can't do anything else.
Then there's the question of "What is jazz?" There are so many kinds of music these days calling themselves "jazz" of one sort or another, that the term has become impossible to define. There are even types of "free jazz" and "experimental jazz" that don't use any of the elements usually associated with jazz, including rhythm! These days, "It's jazz if you say it's jazz".
I think a lot of experimentalists have decided to call what they are doing "jazz" in order to lend a cool credibility and wider acceptability to their music.
It is popular in the theremin community to believe that the theremin can play any kind of music and that it is limited only by the imagination of the thereminist. That is a generous and all-inclusive philosophy, and I can see why so many people subscribe to it. Unfortunately, it's wrong. The theremin is limited by its own innate inability to do certain things, and trying to make it play jazz is like trying to force Cinderella's delicate glass slipper onto Drusilla's great hoof.
Drusilla, of course, will insist that it's a perfect fit because she wants to marry the prince.
Yes, the theremin is a one-trick pony but that trick is so spectacular and unique that it is quite magical when it is done well. We do not do the theremin a favor trying to demonstrate its versatility by forcing it to do things it can't do. On the contrary, I think we do the theremin a disservice and end up marginalizing it even more than it already is. LESS IS MORE.
I've heard lots of theremin fans say that the theremin works beautifully in jazz, but I have never heard a jazz fan say it.