I am an advanced flutist. I am taking Japanese classes, and am going to go to a college where the professor is a native of Japan. What are the chances of getting a job as a professional flutist? I plan to apply for the JET program after I graduate college, for as long as they can take me. To my understanding, the Japanese aren't very welcoming of foreigners anymore.

They are as welcoming as they always are...
And recently lots of foreigners ran away, so there are more opportunities now.

Jet would be the best chance, if you qualify.
Flute would be next to impossible, sorry.

Hmm you could get into an orchestra or something. It's not impossible!

If you sing well you stand better chances but playing the flute in an symphony orchestra to be more exact is also possible. I don't know how old you are but if you have studied or you are studying or will study at Music college or university then that's great!

Search around internet.

The Tokyo Symphony Orchestra
(Tokyo Kokyo Gakudan)

Address: Muza Kawasaki Central Tower 5F, 1310 Omiya-cho, Saiwai-ku, Kawasaki-shi, Kanagawa 212-8554
Phone: +81-44-520-1518
Fax: +81-44-543-1488

Japan Symphony Foundation
(Nihon Kokyogaku Shinko Zaidan)

Address: No. 2 Kameda Bldg. 4F, 2-3-2 Kanda Awaji-cho, Chiyoda-ku, Tokyo 101-0063
Phone: +81-3-3253-2032
Fax: +81-3-3253-0566

Tokyo Metropolitan Symphony Orchestra (TMSO)
(Tokyo-to Kokyo Gakudan)

Address: c/o Tokyo Bunka Kaikan, 5-45 Ueno Koen, Taito-ku, Tokyo 110-0007
Phone: +81-3-3822-0727
Fax: +81-3-3822-0729

I am not sure if these are ONLY for japanese.

Your plan sounds reasonable, just make sure you are extremely good at the flute. I would focus more on that than your Japanese study.

ah, I am studying music education and jazz performance. so I am trying kind of the same thing, I am hoping that there would be a spot in Japan for a foreign music teacher, since I am studying jazz as well, which is something much more unique to America than anywhere else, and would obviously be best taught by an American as it is a uniquely American genre.