The order of flats are B-E-A-D-G-C-F. Going in the opposite direction the order of sharps are F-C-G-D-A-E-B.
To Clear up the # vs. b theory I'll try to give a better and more detailed example. This is referred to as the Diatonic function.
Example: a C# can't substitute for a Db, even though they are identical pitches, because a Db can serve as the third of a Bb minor scale/chord while a C# cannot and the C# can serve as the fifth degree of the F#Major scale while the Db cannot.
Here is the Bb Major scale: Bb-C-D-Eb-F-G-A
Here is the Bb minor scale: Bb-C-Db-Eb-F-Gb-Ab
Here is the F# Major scale: F#-G#-A#-B-C#-D#-E#
Here is the Gb Major scale: Gb-Ab-Bb-Cb-Db-Eb-F
The accidentals for each scale will either be all # or all b, not mixed.
look at the F# Major scale. Something seems strange... E#?????
F# Major is determined in Staff and marked with 6#'s. E# makes the 6th # and follows D#.
If F were used there would only be 5#'s and B Major has 5#'s so you wouldn't be able to determine between the two.
