I guess you could use a script to check the day of the week of all incoming messages, using a rule that runs a script to determine if the received time is on a Friday e.g.
Code:
Sub FlagMessage(olItem As Outlook.MailItem)
With olItem
If Weekday(.ReceivedTime) = 6 Then
' due this week flag
.MarkAsTask olMarkThisWeek
' sets a specific due date
.TaskDueDate = Now + 3
.FlagRequest = "Call " & olItem.SenderName
.ReminderSet = True
.ReminderTime = Now + 2
.Save
End If
End With
lbl_Exit:
Exit Sub
End Sub
You can test it by selecting a message that was received on a Friday and run the following macro.
Code:
Sub GetMsg()
Dim olMsg As MailItem
On Error Resume Next
Set olMsg = ActiveExplorer.Selection.Item(1)
FlagMessage olMsg
lbl_Exit:
Exit Sub
End Sub