why is chrono trigger in final fantasy chronicles?
Because Square needed to re release 2 remakes at once rather then one at a time.

why are the chrono games on every final fantasy site, and vagrant story isn't?
Chrono games are more well known and sold much better and is over all more popular then Vagrant story was. And most FF sites include Chrono games because they tend to make it more of a squaresoft site so they include some of the games by them, but mainly keep it FF.

And the only games that are part of the Final Fantasy series would have Final Fantasy in their names. Chrono is a seperate series made by the same company.