Hungary-Romania
This one troubled me the most and in the end I chose a design focusing on the Danube, the uniting element of the two countries. The six stars are a callback to both nation's old flags.
Balkan Federation (under Bulgarian suzerainty)
Clearly influenced by the EU in terms of design this flag's colors stand for the Balkans (green), peace (white) and bloodshed (red), while the eleven stars symbolize the eleven member states (Slovenia, Croatia, Serbia, Montenegro, Albania,
Pindus, Greece, Bulgaria, Wallachia, Transylvania and Moldavia). The lion head de jure stands for stands for strength, de facto (just like the colors) for Bulgarian domination.
Pan-Fennic Union
The wave/river like bar in the center stands for the maritime tradition of the Fennic states, the colors stand for wealth (gold), the sea (blue) and the winter (white), while the swastika and the Finnish lion stand for the common Fennic identity. The two blue bars at the top and bottom stand for the Arctic and the Baltic Sea respectively.
Pan-Turan Union
The colors red and green stand for Islam, just like the crescent. The four stars stand for the four member states: The (rump) Ottoman Empire, Azerbaijan, Alash Orda and South Turkestan.
United Kingdom of France, Italy and Lotharingia (Rheinland)
For this flag I took some liberties with the terminology. Italy is just confined to the north of the peninsular (thus excluding Two Sicilies) as well as excluding Venetia, while the Rhineland is rather a second Lotharingia consisting out of the Rhineland, Alsace, Lorraine and Belgium (as well as Dutch Limburg). The coat of arms in the center reflects the three member states and French domination. The one in the upper left is the Italian coat of arms, the one in the lower right is the Lotharingian one (very much inspired by Flanders and the Duchy of Jülich). The royal colors of France in this timeline are white, blue and gold. Also of note: France has absorbed the entirety of Navarre though it doesn't have any autonomy like Lotharingia and Italy and is just a regular province.
Holy Union of Malta, Rhodes and Cyprus
The Maltese imagery is a given here considering that these three islands were once controlled by the Knights Hospitaller. The three golden bars stand for the three constituent islands, while the two blue bars stand for the sea separating them.