This is an attempt to capture the median price range for children's illustration. It is not the final word or price fixing.
Some publishers pay less and some illustrators command more.
Sale of original art is a separate transaction. Artist may display the work and retains authorship rights. Under copyright law, artist may reclaim the rights granted after 35 years. Flat fee means that you're being paid a set fee, agreed upon by art buyer and illustrator, that does not include an additional payment of royalties. The artist retains authorship rights.