When you hit a 5 chain, you'll get the gold glittery power which gives you treasure chests for your waits (regardless if you are furiten) if you are tenpai when a hand gets to an exhaustive draw, bar a nagashi mangan for the tiles which you don't have the treasure for yet...
When you hit a 6 chain, you'll get the emerald glittery power which I think gives you double the percentage chances of pulling a tile from a treasure chest that you gain.
For those three powers above, these go away when you fail to extend the chain.
When you level up, you'll get the yellow and red glittery power which I think causes all "dragon points" won from the mahjong rooms (bar the AI rooms, which don't give any) to be increased by 50% for a 24-hour period after you level up. If you level up during this period, that power is extended for another 24 hours.
Please tell me if I've got them correctly, because there are some things which I left out which I clearly have not observed to have happened.