The original post in regards to using a Flugelhorn for this requirement: As it turns out, if you really dig deep, a Flugelhorn IS a bugle based on how the tubing flares out. It has valves which it allows to be a bugle in multiple keys, each key combination creates a separate bugle in a different key. You can play one haunting taps with a Flugelhorn. But, if you want to cut through the crowd and be heard, a trumpet OR A TRADITINAL STYLE BOY SCOUT BUGLE is what you need to cut through. (The traditional 1892 style Boy Scout Bugle is actually a trumpet). I'm just amazed a scout who would have a flugelhorn, would't have a trumpet or cornet...it's sort of a rare bird.
B-Flat, vs C, vs G/F Treble cleft brass instruments are transposing instruments. So when you look at the bugle call music, everything is written in C or so it seems. To transpose this music you simply figure out what key the bugle in your hand might be in, and you write in the upper left hand corner For bugle in the key of and you have now transposed the music. So essentially the C below the staff is the lowest note for the instrument without going into pedal tones (false low notes for lack of simpler explanation). For the Merit badge the notes required are WRITTEN C, G, C, E, G That's ALL and mostly G, C, E, G (Trivia which call uses low C and how many times? hint at: http://scoutbugle.com/MeritBadge.htm)
For why a particular instrument is in a particular key one would have to dig through the history of that instrument and what type of music it was designed to play along with a large dash of tradition. For the starting player, playing a G/F horn makes it simply easier to hit the higher note of the bugle call (G on the staff), so even if playing a a valved trumpet it might be easier to play holding down, let's say, 1&2 valve then playing open. Since the bugler is usually solo, which exact key he's playing in probably doesn't make much difference as long as he can play the notes.
One of the problems though is the scout has to THINK in the lower key if transitioning from B-flat to G an embarrassing example: At a Blue and Gold, when I was a committee chair, I had a G bugle but my brain was still in B-flat. The starting note is a written E which on a B-flat trumpet is very close to the G bugle's written G which is where I started off. Took a bit to get back in key, most of the audience didn't notice, but we had several symphony player who were scouters...A viola player wandered by later..Not many packs have a CLAM BAKE for the Blue and Gold