Not sure which you are asking: A) You want to join an affiliate program that allows people to book flights on your own site and gives you a commission, or B) You already have a GDS connection and you want to start an affiliate program where other sites use your engine and you pay them commissions?
Neither. I want to have a booking engine that compares prices from multiple sites (all of which have an affiliate program). So when someone books clicks on a link to book a flight on my site, I earn commission from whatever site they booked the flight from.
Same as the booking engine that cheapflights.com and skyscanner.com have.
Most likely you'll have to use APIs to hook into the booking engines of the different affiliate programs. On the backend, call each respective API and combine the results before outputting the results to the customer.
You'll have to make sure that doing this is not in violation of each partner's ToS. Many (most?) have language in place to prohibit this type of comparison shopping because of the load it places on their sites.