It's better to call then book on the web site, you simply cannot tell on the web site if the flights you are picking are kids fly free flights or not, since they have a limited number of seats on each flight.
You can also book the "Kids Fly Free" online through Disney (http://bookdlr.reservations.disney.go.com/ibcdlr/en_US/_framework/components/processEngine), and the Disney site DOES show you which flights qualify for the promotion. Note- it works for the Costco and AAA online sites too, since they are all actually going thought the Disney travel company. So if you are either a AAA or Costco member you might want to go that route to get the extra perks with those package. When I planned my upcoming trip, I compared the AAA with Costco, and found that the AAA package was slightly cheaper for my package, so went with them.