Unfortunately, SSRS does not have a double option, but you can use conditional formatting in the text box to control the border.
With your data:

I have a simple table:

, , Name:

Top:
=IIf(Fields!Name.Value = "TOTAL", "Dashed", "None")
:
=IIf(Fields!Name.Value = "TOTAL", "Double", "None")
( ) :

, , MSDN:
Double Line Reporting Service
, 3pt , Preview. Excel .