The closest to an API which aggregates all flights is a Global Distribution System (GDS), of which there are three in common use. Airlines publish their invento

The closest to an API which aggregates all flights is a Global Distribution System (GDS), of which there are three in common use. Airlines publish their inventory on the GDS and travel agents book through them. There are some exceptions. GDS cost money so budget airlines usually don't bother with them. In that case, they may publish an API which agents may consume, or the agent may screen scrape them.