  We study the Hawking flux from a black hole with soft hair by the anomaly
cancellation method proposed by Robinson and Wilczek. Unlike the earlier
studies considering the black hole with linear supertranslation hair, our study
takes into account the supertranslation hair to the quadratic order, which then
yields the angular dependent horizon. As a result, highly nontrivial
kinetic-mixings appear among the spherical Kaluza-Klein modes of the (1+1)d
near-horizon reduced theory, which obscures the traditional derivation of the
Hawking flux. However, after a series of field re-definitions, we can
disentangle the mode-mixings into canonical normal modes, but the reduced
metrics for these normal modes are mode-dependent. Despite of this, the
resultant Hawking flux turns out to be mode-independent and remains the same as
the Schwarzschild's one. Thus, one cannot tell the black holes with nonlinear
supertranslation hairs from the Schwarzschild's one by examining the Hawking
flux, so that the nonlinear soft hairs can be thought as the microstates.
