El Pollo Carlitos is right. Adjectives ended in "e" don't have a gender. As to the Quince or Quinta subject: the Fifteenth is indeed the Quince. But it is incorrect to say "La Quince Brigada", as well as it would be incorrect in English "The Fifteen Brigade". Instead, it should be "La Decimoquinta Brigada". However, this would not fit in the verses. Apparently the authors have taken a poetic license and wrote "Viva la Quince Brigada", after all, they were killing people and there was no time for linguistic refinements.
Un abrazo - Andrés, le toreró de Granada
(*) Curiosity: Escamillo, Carmen's lover in Bizet's opera CARMEN, introduces himself with that phrase (Je suis Escamillo, toreró de Granada) which is a hilarious deformation of "torero de Granada", spoken by a French-speaking baritone in the role of a Spanish bullfighter.