I considered getting an Alaska Airlines debit card a while back (to compliment my AK cc) since I bank at BoA, but after reviewing it-- and other "reward" debit cards, they all don't seem like a great deal.
Make sure you read the fine print before signing up... most only earn you miles or points for signature based purchases (signing the receipt, or pressing the 'credit' button at the store)-- not pin based transactions or ATM transactions. And most stores these days don't even give you the option any more of pressing credit and signing or pressing debit and entering your pin-- they automatically select debit and just require you to enter your pin (and a non-miles qualifying transaction), so since you earn miles on a credit-signature processed transaction, why not just use your miles cc?
Since Citibank is the only bank that offers an AA debit card, I won't be opening a checking account with them anytime soon (especially after seeing their rating on thestreet.com's bank and thrift screener) in the wake of IndyMac and WaMu-- now if there was a way to earn miles by paying your credit card bills, (but I don't know of a way of paying a cc bill with a debit card) I'd be all over that!
Maybe the best rewards option for a debit card is to see if "Visa Extras" is available... but for me I ended up going for the Braves check card just to be different when BoA started offering specialty check cards (go figure!).