Mostly I've heard that people bring their own small camera(s) or use their phone.

 
While a number of the J-girls are JAV models with some videos, most seem to be one or two vids, the agencies are not production businesses and are not going to spend a bunch of money to support the filming. I would expect costs would be much higher as then the agency would be expecting a cut.

 
The girl herself might bring something to control things a bit but similarly, that runs a problem of guys that don't care for the video option then worrying about someone filming them for whatever reasons.

 
Best thing to do is make the investment to see the girl you want for a short session, discuss the options for video and then go back for the session you want to film.

 
There was also some discussion on the USG forums.

and gives it to you at the end of the session.

You bring your own camera. You can record from your phone, camera, etc. Some guys become very creative )