Flower war just sounds silly, but if you can come up with anything better then yeah sure.
That's why I also suggested the Nahuatl word for it: Xochiyaoyotl
I think both work, if
@Gazebo were to change the UA name I bet he would go with 'Xochiyaoyotl', since he seems to favour endonyms, even when the endonyms are awkward for english speakers (e.g. Ger)
On the other hand, Firaxis favoured xenonyms to a fault, even when they sounded stupid or they had to invent them (ie. Pictish warrior, Floating garden). Only one exception to this that I know of (nau vs carrack, even though they were called carracks in Civ IV)
I don't really see a need to change the name of the UA.
Need is an ugly word. This is a video game, we don't NEED the UA to even have a name, or it could be called 'GoogyWoops' for all the difference it made.
Flower wars were ritual wars waged by the triple alliance against neighbouring city-states as a means of collecting captives for living sacrifices, and as a way of demonstrating the Aztec's martial pre-eminence. The Aztecs had a greater population to draw from, so the continuous ritual combat was something that they could maintain at a lesser cost than their neighbours, who had a smaller population pool to draw from.
So flower war reflects both the yields on kill part (collecting captives) and the golden age on winning wars part (regular ritual combat to weaken neighbors). And it reflects the playstyle that this engenders for aztecs (Brief, regular wars with neighboring civs to constantly drain them and establish your preeminence, but never to kill them)