Quick Answer

Now, a certain someone, (yeah, it's you, Logan,) is wondering what to do after you defeat Clair, and how to get her Badge.  Once you beat Clair, go to the Dragon's Den, north of Blackthorn, and get the Dragon Fang.  Also, just a warning, you get into a Multi Battle.  It's you and your rival(mine is Poopy, no really, his name is Poopy,) versus Clair and Lance.  Clair has Dragonair Level 52, Kingdra level 56, and Dragonite Level 60.  Lance has Gyrados Level 68, Charizard Level 68, and Dragonite Level 65.