An iPhone can only stream one "my Photo Stream", and this is bound to one iCloud account, the account that is used for the iPhone.
If you want to stream automatically from one iPhone to several persons using "My Photo Stream", all of you need to use the same Apple ID and the same iPhoto library, because My Photo Stream can only be tied to one library at a time.
With separate iPhoto libraries and IDs use shared photo streams, if your mac supports them, see:
iCloud: iCloud Photo Sharing FAQ
iCloud: Using and troubleshooting Shared Photo Streams