The music and accompaniment are in the book
Solos for the Trumpet Player
(with Piano Accompaniment) Edited by Walter Beeler. Trumpet solo book for trumpet solo and piano accompaniment. 84 pages. Published by G. Schirmer, Inc. (HL.50329980)
ISBN 079355408X. With solo part, standard notation and piano accompaniment. Classical. 9x12 inches.
Here it is listed as a cornet piece (which is also probably historically correct):
Andante et Allegro - Cornet (Trumpet) Solo with Piano Accompaniment Solo Part with Piano Reduction J. Guy-Ropartz Carl Fischer Music Series from Music 44
I think this could also be effective on the flugel. Check out any of the Sergei Nakariakov recordings, the flugel can be awesome even with martial licks!
I do not think you will find any edition of this explicitly for flugel though. Check with the organization running the competition first. I would not turn down anyone with that wish!