Ampacity of Conductive Tape
Your tape's datasheet mentions a resistance of 5 mOhms per square. This means a square of any dimension will have a resistance of 5 mOhms between its opposite sides. 

The way to use this specification is to count how many squares are in the length of your tape. Since it is 12.7mm (half inch) wide, a length of 50mm (2 inches) is 4 squares, each a half inch. Thus the resistance of 50mm of tape is 20 mOhms.

This will be fine for 200mA, the tape will dissipate less than 1mW).

Note you can get this tape for much much cheaper on ebay. Try "slug tape" or "guitar pickup shield tape" or just "adhesive copper tape".