Do you need a drift boat permit to float the box canyon of the Henrys Fork?

No, IDFG does not require a permit to float the Box Canyon.  Idaho Department of Parks and Recreation does require that a boater have an invasive sticker permit before floating.   For motor boats, this is covered in the registration of the boat.  For non-motorized boats, this sticker will have to be obtained from a Parks and Rec office, or at this website:  https://idpr.idaho.gov/Renewal/Default.aspx#