I would like to get the sound from my MacBook Pro to play on my iPhone. For example if I watch a video on my Mac I would be able to view it on my Mac but get the audio through my iPhone. Is this possible?
Yes, you can do it.
You need to be on the same WiFi network and use a pair of matched applications on your Mac and iPhone.
The best known of these are Airfoil (for the Mac) and Airfoil Speakers Touch on your iPhone. See this: http://rogueamoeba.com/airfoil/
Note that Airfoil Speakers Touch does not turn your iPhone into Airplay speakers so you can only stream to it from a computer running Airfoil and not, for example, your iPad.