Here are the two special Classifications of Flizzards. You can't design your own Flizzard in either of these classes, but you can get one through an adopt.

                                                                 Mythic
This class includes dragons and other mythical reptiles. Even Lightfuries and Nightfuries are present in this class.

                                                                    Extinct
This class includes dinosaurs and other extinct reptiles. No aquatic dinosaurs, however, that are already Foxfins.

Example of a Mythic Flizzard: