I have Mail 6.6 on OS X 10.8.5
I have iOS 7.0.4

I am trying to get a handle on flagged emails.

I use Mail and my go-to email provider is Gmail which syncs flawlessly across both devices.

I have, e.g. 3 flagged "accounts" (i.e red, organ & blue) in OS Mail with 2, 83 and 2 emails in them respectively.

Why do these 3 flagged "accounts" not appear in the iOS Mail? I seem to remember there was a limit to the number of mails synced to iOS…does it have something to do with that?

I was experimenting with the flag settings and flagged 1 email in iOS. This synced to Mail and gave it a new color (i.e. red). Then I flagged another email in OS Mail and moved it to the red "account." This synced also from OS to iOS. Is there no way for me to flag mail in other categories from iOS?

I have had my Mac for nearly 4 years so not a newbie any longer, but couldn't even find anything clearly describing this conundrum.