Maybe as follows

Sub ReplyMSG()

Dim testNum As Double
Dim olItem As Outlook.MailItem
Dim olInsp As Outlook.Inspector
Dim wdDoc As Object
Dim oRng As Object
Dim olReply As MailItem    ' Reply
    testNum = InputBox("Enter start number", "Quote Number", 1)
    For Each olItem In Application.ActiveExplorer.Selection
        Set olReply = olItem.ReplyAll
        With olReply
            Set olInsp = .GetInspector
            Set wdDoc = olInsp.WordEditor
            Set oRng = wdDoc.Range(0, 0)
            oRng.Text = "Please refer to this RFQ as Quote #" & testNum
        End With
        olReply.Display
        'olReply.Send
        testNum = testNum + 1
        DoEvents
    Next olItem
    Set olReply = Nothing
    Set olItem = Nothing
    Set olInsp = Nothing
    Set wdDoc = Nothing
    Set oRng = Nothing
End Sub
or if it was only for your use, you could store the number in the registry and lose the prompt e.g. as follows
The registry entry is at HKEY_CURRENT_USER\Software\VB and VBA Program Settings\ReplyMsg\

Sub ReplyMSG()

Dim testNum As Double
Dim olItem As Outlook.MailItem
Dim olInsp As Outlook.Inspector
Dim wdDoc As Object
Dim oRng As Object
Dim olReply As MailItem    ' Reply
    testNum = GetSetting("ReplyMsg", "Settings", "Quote Number", 1) '1 is the start number
    For Each olItem In Application.ActiveExplorer.Selection
        Set olReply = olItem.ReplyAll
        With olReply
            Set olInsp = .GetInspector
            Set wdDoc = olInsp.WordEditor
            Set oRng = wdDoc.Range(0, 0)
            oRng.Text = "Please refer to this RFQ as Quote #" & testNum
        End With
        olReply.Display
        'olReply.Send
        testNum = testNum + 1
        SaveSetting "ReplyMsg", "Settings", "Quote Number", testNum
        DoEvents
    Next olItem
    Set olReply = Nothing
    Set olItem = Nothing
    Set olInsp = Nothing
    Set wdDoc = Nothing
    Set oRng = Nothing
End Sub

Sub ResetStartNum()
    SaveSetting "ReplyMsg", "Settings", "Quote Number", 1 '1 is the start number
End Sub