Hm. I posted a reply, but it seems to have gone to somewhere else. I'll try to remember what I wrote before and repeat.
I don't see a problem with that, so long as they have good technique and can teach it to you.
My first private teacher was a college gal on the street behind mine. I think she did a good job of advancing me beyond the basics I learned in elementary band (which teacher was a flutist herself, so I may've gotten better training than the average). After that was a lady at church, then the same band teacher until I graduated h.s.
Just be sure you like working with him/her, and after a few months assess if you feel you've learned anything, your skills have advanced, and your playing seems better.
1975 Gemeinhardt M2 in chrome nickel
1982 Armstrong 80
2006 Yamaha 584
1978 Artley piece of crap 15 P
1982 Gemeinhardt 4S
1980s (?) Armstrong all wood (no model)
2006 Jupiter di Medici G0199
Plus many many flute-cousins....