Mad Maudlin has perfectly stated the rules, so here are the exceptions:

If the name of the chord is a vowel, then for 'flat' you do not add 'es' but just 's', so Aflat becomes 'As' and Eflat 'Es'. Pronounciation guide for Ais and Eis: pronounce the vowels separately.

H (which is termed B for you) in the flat mode does not become Hes, but B. So your B is our H and your Bflat is our B. Easy, eh?

Wolfgang