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".

The thickness is 0.0026in and 0.5in wide. This means it has a cross sectional area of 0.00115in^2 which corresponds to AWG18 or AWG19 wire. So if the resistance is the same (which it should be pretty close if both are made from copper) then it would be acceptable to compare the cross sectional area.

Powerstream says 14A is the max, but it really depends on how high temp is acceptable for your application. I'm willing to bet copper tape will dissipate heat to air (or metal) more readily than a wire, and could possibly tolerate more current than 14A

A 12.7x0.04mm, 0.508mm2 copper section, should be similar to a 20 AWG cable, 0.033 \$\Omega\$/m, with a 5.0 A Ampacity (NFPA tables, 90 deg., Single Conductor, Insulated Ref.3).

Assuming the 12.7x0.026mm, 0.3302mm2 acrylic conductive section have less than 50% conductivity of copper, we could safely assume the tape is similar to a 19 AWG cable, with a 6.0A Ampacity (Interpolated, NFPA tables).

As reference, the NFPA ampacities are more conservative than the NEC ampacities, i.e. a 12 AWG cable has 20 A Ampacity (NFPA) vs 30 A (NEC) for 90 deg.

Remember those ampacities are for single conductor, insulated. In this case the conductor is "half insulated", which should give an additional margin.