Thanks for the reply, Jenny.
I searched BigFish and they don't list the Flash Player as a requirement for any of the 6 games. But some games that use QuickTime don't list it as a requirement either.
I did a search of the BF Forums on Flash Player. It listed a number of posts from players of the various Dream Chronicles that they received an error message about their version of Flash Player.
As far as I can tell, it looks like it's not required for the Azada series but is for the Dream Chronicles series.
Thanks again Jenny and Marian.