Perhaps something like:
Option Explicit
Private WithEvents inboxItems As Outlook.Items
Private Sub Application_Startup()
Dim outlookApp As Outlook.Application: Set outlookApp = Outlook.Application
Dim objectNS As Outlook.NameSpace: Set objectNS = outlookApp.GetNamespace("MAPI")
Dim ShrdRecip As Outlook.Recipient: Set ShrdRecip = objectNS.CreateRecipient("someone@somewhere.com")
Set inboxItems = objectNS.GetSharedDefaultFolder(ShrdRecip, olFolderInbox).Parent.Folders("Sent Items").Items
End Sub
Private Sub inboxItems_ItemAdd(ByVal Item As Object)
If InStr(UCase(Item.Body), "HI") > 0 Then
Item.FlagRequest = "Follow up"
Item.FlagDueBy = DateAdd("d", 2, Date)
End If
End Sub