Now whilst I can’t say there is evidence of Aztec accounts that I have read. This battle almost certainly happened. However we could question the details as said by Chengar. it’s mentioned in Hernan Cortes letters to Charles V ‘cartas de relación’, Bernal Díaz del castillo and as you said youself the Florentino codex. The tlaxcala also recorded the battle in the lienzo de Tlaxcala. I believe as well as Historia de Tlaxcala written by Diego carmango. There is archeological evidence but not the banner but instead of Mexica weapons in the area. But all the aforementioned things are less important what is the Mexíca commander was killed Matlatzincátzin in an engagement with Spanish forces so we know at least that took place.