I am looking to get a double mastectomy for mostly cosmetic reasons, would a surgeon perform this?

Having a bilateral mastectomy in order to become a ballet dancer is far too radical! Testing for the BRCA gene might help decision making if you are positive, but the sad truth is that most hereditry breast cancer is not actually BRCA related and cannot be tested for.
A breast reduction down to an A cup would seem most appropriate assuming that this would match your body habitus. (I cannot imagine you are anything but extremely slim, the D cups notwithstanding).
As for the family history of breast cancer, you will need routine mammography and should learn the technique of self examination.

This is possible to undergo bilateral mastectomy prophylactically in patients at high risk of breast cancer with immediate reconstruction. In your case, if there are no cancer risk concerns, the better option would be to undergo either breast reduction or ultrasonic liposuction of your breasts. Best of luck in your acceptance to the ballet school.

Congratulations! That is so exciting! And yes smaller breasts are definitely considered the ideal for a ballet dancer's body. It is important with your family history that you do see a physician and undergo testing/evaluation given your family history of breast cancer. Obviously if the testing comes back positive then a mastectomy would be recommended but if it does not, then this would be a somewhat drastic surgery. I'm not sure if you have been exposed to a women who has had a bilateral mastectomy, but it is not the same as just having small breasts. Many women feel very self conscious after this procedure. A breast reduction could give you small breast that would still look very feminine and retain your nipple/areola complex.

If you wind up considering an actual mastectomy, having on opinion from a breast oncologist will help sort out the options, and if indeed your are even a candidate for such a procedure.An alternative that sounds more acceptable, at least to me, would be a breast reduction, and for that you would see a plastic surgeon.But given your family history I would not toss out the option you have suggested without a proper evaluation.Thanks for your question.  Good luck in Russia!