Sassy, I don't know if you are a client of BK, but if so, there is a lot of helpful information regarding Regent's air program on their website at http://www.bkrssc.com/I_Air_Information.htm

I always start by doing my own search to see if the price is better through Regent. Since I usually come in early, that means a "deviation" fee for Regent air, and the added cost of a transfer to a hotel and then to the ship. Also, now I believe taxes for the flights are added to your invoice, but you would need to check with your TA for confirmation.

Getting mileage for Regent air is up to you, and not generally allowed because Regent gets contract prices on their flights. They use a variety of airlines.