If you set it up as IMAP you don't get push.Is you Google Apps email set up as Exchange? Flags seem to work fine for me in both iOS 8.1.2 and Mac OS 10.9.5 with GApps set up as IMAP. At Gmail, in my Settings>General>Stars, I have one Star (flag) in use.
However, my Office 365 email account (Exchange) exhibits the behavior you are describing...sometimes. Today, flagging on any device is showing up everywhere.
So it could be a GApps/Exchange issue if you have it set up that way.