You can do it with a script associated with a rule to process incoming messages. e.g. the FlagFriday macro below. I have included a macro that will enable you to test on a message in your inbox. Messages sent on Friday are flagged.
Because of Outlook security, you will almost certainly need to self certify the vba code -
http://www.gmayor.com/create_and_employ_a_digital_cert.htm
Code:
Sub TestFlag()
Dim olMsg As MailItem
On Error Resume Next
Set olMsg = ActiveExplorer.Selection.Item(1)
MsgBox Weekday(olMsg.SentOn)
FlagFriday olMsg
lbl_Exit:
Exit Sub
End Sub
Sub FlagFriday(Item As Outlook.MailItem)
If Weekday(Item.SentOn) = 6 Then
Item.MarkAsTask olMarkToday
Item.Save
End If
lbl_Exit:
Exit Sub
End Sub