It's quite clear that the Monarchy of Gryz is, as you may have guessed, a monarchy. The crown stands for monarchy, and besides that, for kings, queens, or other royal people. Purple also stands for kings, queens, and royal people. The orange may refer to Carthago, and the yellow perhaps to the Ptolemaic Empire. Others say that the orange and yellow simply represent gold, and gold is associated with monarchies. The orange isn't Carthaginian orange, anyway, although the yellow is Ptolemaic yellow. Another interesting thing is, that there is no sun or circle on the flag (unless you count those on the crown), which is quite unique for Ptolemaic rebel nations.