After a request by reader Bruno Rodolfo, I decided to make a new flag for the province, with more references to provincial history.
This is the current flag:

It was adopted in the 1990s. I think the design has some merits, but the color clash is problematic.
My humble take on this thread is the following:

The diagonal layout remembers the map of the province. The medium blue fields represent the sky — "buenos aires" means "good airs" in Spanish — and the sea, respectively. The white stripe is not only a nod to Argentinean flag, but a reference to Plata river — "plata" is Spanish for "silver —, fundamental for the development of the province and the whole Argentina. The golden color represents province's wealth, and the red demi-sun is a symbol of federalism and appeared in earlier Buenos Aires flags.
Comments and suggestions are welcome.
Many thanks for reader Bruno Rodolfo, for his valuable theme suggestion.