You might want to look into "points" based credit cards. These aren't tied to a specific airline, and you accumulate points or miles, but then use the card's website to book travel with your points. Basics are that $1.00 purchased equals from 1-2 points/miles. Each of these turn into $.01/.02 of a ticket price.

So for example you spend $40,000 on the card, and receive 80,000 points. After a while when you're ready to redeem you can book a flight to anywhere and if the fare is $1400 you can use 80,000 in points to reduce the cost of the fare by $800. The flight will now cost you $600. These types of cards don't offer the absolute best redemption values but can help in certain situations.

Look into:

Capital One Venture 2 points per $1
Chase Sapphire Preferred 2 points per $1

Sadly both of these cards just offered a chance at their biggest sign up bonuses ever (100,000 points=$1000 in flights), so it might not be the best time to go for them. That said there are other cards out there that allow more flexibility (AMEX Member rewards points I believe also).