Looks like you need to specify all the borders in order to get a match.

   Application.FindFormat.Clear
   With Application.FindFormat.Borders(xlEdgeLeft)
        .LineStyle = xlDouble
        .ColorIndex = 1
    End With
    With Application.FindFormat.Borders(xlEdgeRight)
        .LineStyle = xlDouble
        .ColorIndex = 1
    End With
    With Application.FindFormat.Borders(xlEdgeBottom)
        .LineStyle = xlDouble
        .ColorIndex = 1
    End With
    With Application.FindFormat.Borders(xlEdgeTop)
        .LineStyle = xlDouble
        .ColorIndex = 1
    End With
    Set aRange = Range("Data").Find(What:="", After:=ActiveCell, LookIn:=xlValues, LookAt:= _
        xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, MatchCase:=False _
        , SearchFormat:=True)
Also not the Top edge border is fussy about where in the code it sits.