I wouldn't use a tile-editor for a game like chess. The board is really simple and you can easily draw it without the help of a tile-editoeeditor. These maps make much more sense if you have a large world/board with lots of different tiles.
I don't know the GeekGameBoard you linked to, but it looks like it's a framework for card and board-games, so this seems much more suited for your task. It seems like this framework provides several UI elements, so you'll probably either choose GeekGameBoard or Cocos2d. Mixing the two would most likely force you to rewrite/refactor a lot of the GeekGameBoard code (which might be more work than starting your game-code from scratch).