When using the spell-checking feature of M-x checkdoc, if flyspell-mode
is enabled then the checkdoc-ispell-lisp-words are not recognised as
correct.  For example with the foo.el below

    (progn
      (setq checkdoc-spellcheck-documentation-flag t)
      (find-file "foo.el")
      (turn-on-flyspell)
      (checkdoc))

    => asks to correct spelling of "keymap"

It looks like checkdoc-ispell-init assumes that if an ispell-process
exists then it was checkdoc-ispell-init which started it and therefore
doesn't need the checkdoc-ispell-lisp-words sent again.  Of course
that's not the case if using flyspell, and presumably also not if you
use ispell.el directly and still have the process running.

Perhaps a flag meaning "checkdoc-ispell-lisp-words already sent" could
to be attached to the process object, to send just once.  Does it hurt
to send the words more than once?  The simplest thing could be to just
send them every time.