I don't always agree with those green squiggly lines, but in this case I wholeheartedly concur.
Remember, in the phrase he himself, we are using the "himself" to put emphasis on the fact that it was "he" who did the work.
OK: He made forty drawings for the book and traced them for their lithographic reproduction.
(the and joins the verbs made and traced; he is the subject)
OK: He made forty drawings for the book, and he traced them for their lithographic reproduction.
(the and joins the two sentences; the and could be removed and they could be separated by a semi-colon instead of a comma)
OK: He made forty drawings for the book and traced them for their lithographic reproduction himself.
OK: He made forty drawings for the book and he traced them for their lithographic reproduction himself.
OK: He made forty drawings for the book and he himself traced them for their lithographic reproduction.
All of these work; the himself simply adds extra emphasis to the subject he.
NOT OK: He made forty drawings for the book and himself traced them for their lithographic reproduction.
Your variation doesn't work. We expect a new subject after the conjunction and, or else a second verb that is joined with the first verb. The word himself can't act as a verb or as a subject, so your sentence is jarring to the ear.