I assume you want to loop through all the feature classes you're collecting, so it should be:
# we only need to do this once
hkfc = "C:\Wiley\P1\gis\HK80.gdb\Building_merge_dissolved"
desc = arcpy.Describe(hkfc)
spatialRef = desc.spatialReference
for input in fc:
output = os.path.join(outdir, os.path.basename(input) + "_project")
arcpy.Project_management(input, output, spatialRef)
The way you're using walk
is a little awkward but should be functional.