Try the code below.  Just change anything you need to in the calling MyMacro
procedure:

Sub MyMacro()
On Error GoTo MyMacro_Error

   Dim objInbox As Outlook.MAPIFolder
   Dim objNS As Outlook.NameSpace
   
   Set objNS = Application.GetNamespace("MAPI")
   Set objInbox = objNS.GetDefaultFolder(olFolderInbox)
   SearchFolderForMessagesFlaggedForFollowUpBeforeSpecifiedDate objInbox,
#01/30/2005#
   
   Set objNS = Nothing
   Set objInbox = Nothing

   On Error GoTo 0
   Exit Sub

MyMacro_Error:
   If Err.Number <> 0 Then
       MsgBox "Error " & Err.Number & " (" & Err.Description & ") in
procedure MyMacro of VBA Document ThisOutlookSession"
       Resume Next
   End If
End Sub

Sub SearchFolderForMessagesFlaggedForFollowUpBeforeSpecifiedDate(MailFolder
As Outlook.MAPIFolder, BeforeDate As Date)
On Error GoTo
SearchFolderForMessagesFlaggedForFollowUpBeforeSpecifiedDate_Error

   Dim objItems As Outlook.Items, objMailItem As Outlook.MailItem
   Dim strCriteria As String
   
   strCriteria = "[ReceivedTime] <= """ & BeforeDate & """ AND
[FlagRequest] = 'Follow up' AND [FlagStatus] <> 1"
   Set objItems = MailFolder.Items.Restrict(strCriteria)
   
   For Each objMailItem In objItems
       objMailItem.FlagStatus = olFlagComplete
       objMailItem.Save
   Next

   On Error GoTo 0
   Exit Sub
   
   Set objItems = Nothing
   Set objMailItem = Nothing

SearchFolderForMessagesFlaggedForFollowUpBeforeSpecifiedDate_Error:
   If Err.Number <> 0 Then
       MsgBox "Error " & Err.Number & " (" & Err.Description & ") in
procedure SearchFolderForMessagesFlaggedForFollowUpBeforeSpecifiedDate of VBA
Document ThisOutlookSession"
       Resume Next
   End If
End Sub