Excluding books read on a computer, the first I read on a portable device was... I can't actually remember
but I read it on a Psion 3c some time in the 90's.
Having a hard time remember the first book I read on an eInk based reader (which was my Hanlin V3 mid-2008), possibly a book from the Honor Harrington series, pretty sure I started reading those on and off before buying an eInk device. Reading Echoes of Honor currently after having a break from the series for quite a while.