It's a white background, with the arms of the Baron of Rio Branco (1845-1912), including the barony crown (!) and his personal motto ("Ubique Patria Memor", that means "Wherever I go, my patria will be on my memory"), that's also Rio Branco municipal coat of arms, and the letterings "MUNICÍPIO DE RIO BRANCO" ("Municipality of Rio Branco") on top and "ESTADO DO ACRE" ("State of Acre") on the bottom.
From now, I think the origin of city's name is clear. The Baron of Rio Branco, son of the Viscount of Rio Branco (the longest serving prime-minister of Empire of Brazil), was a Brazilian geograph, historian and considered the "father of Brazilian diplomacy", for his work on border disputes (including the case of Acre, hence the tribute on the capitol of the state). His popularity was gigantic: his name was quoted to the presidency and, when he died, the Carnival was paralysed for mourning. Currently, his face appears on Brazilian 50 cents coins. He's also related to vexillology: he made a proposal to a new national flag.
The arms of baron of Rio Branco is a simplified version of the arms of his father (that also included a feather and a compass). It's constituted by the a golden armillary sphere of blue interior (heraldically related to Brazil) and a silver river (canting, as "rio branco" means "white river").
My proposal is a banner of arms of the municipality, identical to those of the baron:
This flag has all the necessary symbolism of current flag, but it's much more direct to the point. The flag is slightly similar to the one of the Kingdom of Brazil (1815-1822), but I don't know if it's a problem at all.
Your comment is welcome!
If you want to know more about Brazilian nobility, click here.