My son has not used Flonase, but he has used Nasonex which is also a corticosteroid nose spray.  You may want to keep an eye out for symptoms of oversuppression, but other than that, I don’t think there is really too much to worry about.  If the combination of nose spray and oral hydrocortisone proves to be too much corticosteroid, then maybe you can talk to your endo about reducing the hydro dose to compensate, at least temporarily?