It's possible to control the music onto your phone with the Blaze, though the Blaze itself isn't capable to store / play music on the tracker itself since not having the hardware to do.
Feel free to check out the Fitbit Article on how to set up your Blaze for music control on your phone:
http://help.fitbit.com/articles/en_US/Help_article/How-do-I-use-my-tracker-to-control-music
