Is it safe to use foil heat tape inside the dryer?
To be absolutely clear, this duct carries the fan-blown and lint-filtered air coming OUT of the dryer drum. It is NOT the duct carrying the heated air into the drum.
Given that, the upper working temperature of that tape is listed as 200°F. My guess is that this is above the max temperature of the air coming out of the dryer, but I'm not sure. At worst, the adhesive would fail; I doubt you'd have a fire hazard, especially since the environmental lint, which would be far more flammable, isn't expected to burn.