Doesn't work with an Outlook Exchange Account either.
I have my companies email going to my phone and I can not flag emails in Outlook on the phone.
So guessing this is an issue with mobile outlook and not so much an issue with the method of getting the emails.
EDIT: Looks like I jumped the gun a bit on this. Per Microsoft
http://msdn.microsoft.com/en-us/library/bb158527.aspx you can flag emails on Outlook Mobile but ONLY if using an Exchange account and Exchange is version 2007. Company I work for is on Exchange 2003 and don't see them going to 2007 anytime soon...