How to listen to the same song at the same time on 2 different iPhones?
There are couple of young coders who met at 2013 WWDC after getting a scholarships from Apple who had the same idea you describe. They brought out an app called
Audibly

Description
Audibly plays your music in sync across nearby iOS devices. Just
choose the songs you want, link up some devices, and you're ready to
go.
Hanging out with friends and want to play a song, but your phone’s
speakers aren't loud enough? Instantly create a wireless surround
sound system and forget messy headphone cables.
Features: • Create a playlist of songs from your own library • Control
the volume across all the devices • Music kept in sync as you listen •
Use filters to change the pitch of the music • Favorite what’s playing
to come back to it later • No Internet connection required*
Audibly was first created at WWDC by a group of Student Scholarship
Recipients: Nick Frey, Chris Galzerano, and Veeral Patel.

Music can be streamed over Peer-to-Peer Wi-Fi on newer, supported devices, anywhere you are without an Internet connection. Devices can
also connect over a Wi-Fi network.


They still have some bugs to iron out but I have used it and it works well.