Equivalent of millis() in Atmel studio
The millis() function is defined in the Arduino Core for AVR architecture, specifically the wiring.c file.

You can see that timer0 is setup with various parameters for prescaling and interrupt triggering and handling of timer0 overflow such that a variable called timer0_millis contains the number of milliseconds since the sketch started. 

The millis() function basically returns that timer0_millis value.

If you wish to make use of the function in AVR Studio, then you would need to include the same kind of timer0 setup and interrupt/overflow handling that the Arduino core does.