We demonstrate a chip-scale scheme of Brillouin instantaneous frequency measurement (IFM) in a CMOS-compatible doped silica waveguide chip. In the chip-scale Brillouin IFM scheme, the frequency-to-power mapping process is achieved by one-shot detection without additional time averaging and implemented by lock-in amplification, which successfully detects the Brillouin gain of the doped silica waveguide chip in the time domain. A Costas frequency modulated signal ranging from 8 GHz to 9 GHz is experimentally measured, and the frequency measurement errors are maintained within 58 MHz.