Mail applications work slight different than an app like calendar, but it very easy to manage your mail through all devices/computer.
As Allan stated, you need to have your mail set up as as IMAP or Exchange. If you are using POP for your mail, you cannot easily have all devices managed automatically.
To put it simply, POP Mail is stored locally, so runs independently, where as IMAP and Exchange mail, store the mail on a server, so each device that is connected to it is automatically updated to the same state. Examples of IMAP accounts are iCloud and Gmail, however, most service providers offer IMAP services.
Flagging of mail is currently available on the iPad and iPhone. When you have an email open, touch the Mark link and you are presented with Flag/unflag or Mark/Unmark. If your mail is set up as say IMAP, when you flag a message there, it updates your other devices. I cannot test Outlook as I do not use it, but see no reason why if the mail accounts are running as IMAP or Exchange, why this would not work too.
Hope this helps