Sorry, there is no storm chasing career field. The few individuals that do it are:
1. Chase tour operators. You may get hired as a driver. However this work is very seasonal and positions are hard to find. If your entrepreneurial skills are sharp and you have chase experience, you may be able to run a chase tour business yourself. However, again, the work is seasonal and the overhead costs stack up fast. It's only a career for those who put 100% into the business.
2. Scientific researcher. You have to have the right skills and education. Sometimes volunteers are accepted for chase work (such as in the IHOP project). However paid positions are limited to participating faculty members such as those of OU, as well as researchers at agencies such as NSSL. Your best chance of landing a paid job as a researcher is to work towards, at least, an MS degree in atmospheric sciences.
3. Photographers/journalists. You must already have a career in photography or journalism to get paid chasing, and of course you must be working for an employer who is interested in storms as an assignment (or you must be freelancing).
Another would be Media (TV stations), but it's part time at best and generally only gas costs and meals. On the down side, your limited in where you can go. On the up side, you get a support system that is usually pretty good. Doing it full time? NOt very many, but I do know a couple that work for the larger TV Station in OKC. They're getting to be few and far between though.
This spring I started working as a stringer storm chaser for KWWL Channel 7-Waterloo Iowa, I have averaged between 50$ and 100$ for each video I have brought in. Not expecting to get rich but atleast it helps get me name recognition, lets me share my videos with the public, and pays for my gas etc.
I just managed to make nearly $400 for some video shot of Frances and my Storm Chasing trips in 2000 or 2003 for a TV show being aired here soon. It's hard and certainly not the main aim of why I chase.
I chase for a local TV station here in Amarillo and make enough money to cover the cost of gas and lodging through the season. I freelance for them so I am not limited to where I can go which is obviously a good thing. If I was limited to where I could go, I don't think I would be chasing for the station.