From the video: "Pycnoporellus fulgens". It does look the same fungi to me. How exciting! I never knew you could dye with fungi, but there is a society dedicated to the
art:
http://sonic.net/~dbeebee/IMDI.htm
It seems quite easy according to
http://www.somamushrooms.org/dyes/ just chop the fungi up and heat them in
water to extract any colour they may have. From the same site it suggests that bracket fungi like that are good for paper making too, so if they are no good for a dye colour, you could always try that.