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.
Flutes:1975 Gemeinhardt M2 in chrome nickel;1982 Armstrong 80;2006 Yamaha 584
Piccs:1978 Artley piece of crap 15 P;1982 Gemeinhardt 4S;1980s? Armstrong all wood (no model)
Bass:2006 Jupiter di Medici G0199
Treble:20?? Guo New Voice
+ many flute-cousins