I was just researching the same thing. It seems that Kayak actually searches a large number of other sites to provide their pricing comparison results. Kayak itself has an api which is apparently no longer available for use, due to costs of misuse...but many many travel sites do the same thing as affiliates for other sites like expedia, viator, tripadvisor etc. Most of these have both affiliate and partner agent options. You might want to look at this link: http://www.programmableweb.com/news/5-travel-apis-comparison-to-booking/2007/10/29
Many of the sites also offer a white label website that will auto-update prices etc. and that allow you to make them look, fit and plug into your own site. There are also wordpress themes specificially designed to fit this...some free, some premium.
In addition to that, if you are not a travel agent, there are still ways to act as one with full licensing and use of sabre etc.
Most sites, kayak included, use these options with some complex programming, because, as @briantopping noted, establishing partnerships with that many hotels, airlines, etc. isn't something most individuals can manage...and even if you could, the big sites have higher commissions, because between massive advertising campaigns, thousands of employees, and tens or hundreds of thousands of affiliates, they drive the most sales. Hope that helps.