Sorry, something got screwed up in my post:

"Let's try another scale: Eb major which has three flats according to that chart. Which notes in that scale are flatted? Eb (1), F (2), G (3), Ab (4), Bb (5), C (6), D (7) and Eb' (8). So there are our flats in Eb major—Eb, Ab, Db."

Of course that should read Bb, Eb and Ab. Sorry for any confusion.