On my Mac, I’ve checked “Today includes Flagged items”, which is a very useful option for me. But in iOS, flagged items do not show up in Today, and I can’t find the option to choose that.
So flagged items are shown as Today items on my Mac, but not on my iPhone for iPad.
The ability to display flags in the Forecast perspective is a new feature that’s making its debut in OmniFocus 4. This pre-release software is available through TestFlight on iPhone, iPad, and Mac.
It sounds like you’re running OmniFocus 4 on your Mac and OmniFocus 3 on your iPhone/iPad. If so, if you install/open TestFlight on your iPhone/iPad, you should see OmniFocus 4 waiting to be installed.