The image needs to be added and then hidden. It will be added and hidden at position 0.
.Attachments.Add Fname, 1, 0
The 1 is the Outlook Constant olByValue
Once you add the image then you have to use "cid:FILENAME.jpg" as shown below.
Try this:
With OutMail
    .To = tName
    .CC = ""
    .BCC = ""
    .Subject = STAT.Range("C1").Value
    .Attachments.Add Fname, 1, 0
    .HTMLBody = "<html><p>Summary of Claim Status.</p>" & _
                "<img src=""cid:Claims.jpg""height=520 width=750>"
    .Display
End With
Screenshot
