Monarchy: It's a simplified version of the Latin Empire CoA, but with Greek colours. This serves to represent a combination of Catholic (West) and Orthodox (East) symbols, to represent Constantinople being an "International" and "Neutral" city kind of thing.

Republic: The main symbol of the sun/star and crescent, as you all know, wasn't originally a muslim symbol, but rather the banner of Constantinople. It's now shared meaning with Islam would, in this flag, represent not only the city itself, but also it's shared past of both Christianity and Islam, which is something a republic would be more readily accepting of rather than a monarchy. The nine stripes were used extensively by the greek cultured population during a lot of years of the Ottoman period to this day, their origin is unknown though.

Communist: Since Constantinople guy wanted a more down-to-earth thing I made this one. The two red sides represent the two coasts of the city, while the blue stripe represents the Bosphorous. The anchor was a symbol during the greek revolution and represents labour and steadfastness of purpose. The second one is the one I suggested in the first place, you can find its meaning in the pack's pdf.

Fascist: These are flags I used for other things but I think both could serve its purpose well in this one. The first one uses the Orthodox Double Headed Eagle as a base, with no crown, and a shield in its chest with the flag raised by Andreas Londos at the outbreak of the Greek War of Independence. It also takes the latter’s colour palette. It turns out that by pure coincidence, a very very similar flag is used currently by some fascist groups in modern Greece.
The second one is the same but instead of Londos' cross, it uses a Chi Rho, early symbol of Christianity, used extensively by Emperor Constantine I.

Theocracy: The symbol of the Patriarchate of Constantinople over a pure white field. Simple enough.