Here are two flags I did for my A More Personal Union
This is the flag of the Golden Roman Empire, basically an independent New Spain. The gold is for the Golden part, obviously, and the Tyrian purple is to evoke the Roman Empire. The Cross of Burgundy was used for three reasons: 1) it is associated with St. Andrew, who was the founder of the Church of Byzantium, and Emperor Ferdinand sees himself as the successor of Constantine, 2) it was traditionally used on the flags and arms of New Spain and various other Spanish colonial possessions, and 3) as JackTheCat pointed out, it looks like two crossed macuahuitls, which are obsidian-edged weapons used by various Nahuatl-speaking cultures, and Ferdinand has based his empire on a warrior caste comprised of assorted Mexica, Maya, Tlaxcalans, etc.
This is the flag of the Most Christian Republic of Naples, which is an ecclesiocracy in southern Italy. Since the republic was founded amidst a backlash of anti-foreign sentiment, all the previous Neapolitan flags, which drew attention to various foreign overlords, had to be scrapped, and so this design is new. The white field indicates Christ, his sacrifice, and the purity of the new state. The scarlet cross potent is the color associated with Cardinals of the Church, since the leader of the new government is a Cardinal; it also brings to mind Christ's blood. The cross itself evokes the Jerusalem (or Crusader's) Cross, signifying the Neapolitans' view of themselves as carrying on the work of "crusading for Christ", albeit in a non-violent way.