All these name stories are fascinating. I appreciate them. As promised, here's a the story about my flags. All of them can be viewed here:
https://www.nationstates.net/page=dispatch/id=1343089
So, my first flag ever was the Greek flag because I had an interest in Greek democracy and philosophy. As mentioned in the OP, this turned into my RP inspiration.
While trying to learn how to worldbuild, I created my second flag: "Kallipolis Wanderer". I had the idea to put my iRP capital on a mountain and added in the Parthenon-style Capitol. Kallipolis means "beautiful city" in Greek, and I thought it was quite fitting. Even today, the Evrigenese capital in NS is Kallipolis! I was also inspired by the style of "Wanderer above the Sea of Fog", so I added a nod to that in the title. I later decided that "Kallipolis Wanderer" wasn't very flag-like and wanted to keep it in a different form. (Those of you who know me on Discord are familiar with a reincarnation of KW, but I didn't join Discord until much later).
At the time, I had just unlocked the custom banner page and was excited to place it there. However, I had to replace it with something interesting. To keep with the Greek theme, I started with a tricolour of blue and white. The white stared back at me, begging to be filled. An emblem looked just about right. I chose the unequally sized Borromean rings to represent the three branches of government. They are intertwined yet separate, and obviously different sizes. Each ring is in one of three primary colours of computer screens (Red, Green, Blue) to represent the prominence of the Information Technology industry. I further added a rounded triangle to symbolize unity.
What's your flag story? I'd love to hear it! If you weren't here for the first time around, please share your name story too!