I'm happy to pay to use a flight search API. Kayak and Hipmunk could provide an API and pass on the cost to the API consumers.
How will the API consumer make money? I don't think Ads will generate enough revenue -- especially not on mobile.
Kayak will get some revenue from the bookings resulting from the searches, and would need to circle back some of this revenue back to the API consumer. This is technically complicated because it requires a lot of tracking infrastructure.
In the end, a service that would make sense is a lot more complicated than simply having an endpoint and saying it's X dollars per Y calls.