I have started playing guitar in a concert band in which almost all of the music has no guitar parts. Are there any other instrument parts I can play without having to transpose?
Yes and no.
You can play any treble clef line for a non-transposing instrument (violin, piano, xylophone, flute, etc.). You'll sound one octave lower than written - the guitar transposes at the octave.
For other instruments (saxophones, clarinet, trumpet, etc) you'll need to transpose. How far depends on what the instrument is.
Guitar teacher offering lessons in Plainfield IL
I have started playing guitar in a concert band in which almost all of the music has no guitar parts. Are there any other instrument parts I can play without having to transpose?
How did playing the flute part work for you? What sort of concert band is it? Your best bet may be to find the lead sheet or just the chords of the songs your band is playing and comp. The horn/string part that you transpose can be the basis for a solo.