Brasília is of course a city characterized by its modernist design and architecture, and its geometric layout, so its not more than logical that the flag has a similar feel to it.

The flag was designed by the poet Guilherme de Almeida. The Cross of Brasília in the center symbolizes the indigenous heritage and the strength that hails in all directions. The white background of the flag stands for peace, and gives the idea of infinity, or the vast Brazilian territory. The green and yellow colours in the middle refer to the most commonly used of the four colours of the national flag to represent Brazil. The four yellow arrows symbolize the native nations of Brazil, whereas their pointing into the four cardinal directions of the compass stands for the centralized emanating political power of Brasilia, as the capital of the country. The yellow arrows also form a cross, which symbolizes both the Southern Cross. With their feathers, the arrows form a lozenge in the middle, a reference to yellow lozenge of the national flag.

Before 1969 this design was used:

Wikipedia article about the flag