In the mid-1800s, British soldiers in started dyeing their uniforms to a dusty color. They named the color 'Khak' which is an word used for dust, soil or ashes in many indian languages. Later some time, khak colored uniforms became official. The word khak later became known as 'khaki'.
One of the biggest reason of khaki uniforms still being worn by indian police is that though british left our country but many laws and organizational rules that were made by them, haven't been changed. Still to this day, uniforms and their color, drill movements and commands haven't changed much.
The color khaki also has its own benefits. Khaki cotton uniforms are cool, cheap and don't show dirt and dust. British people left india in very poor and devastated conditions. So the khaki uniform was probably a better and cheaper choice for the indian population that was economically not very strong at the time.
Information Source:- "Khaki Uniform 1848–49: First Introduction by Lumsden and Hodson", Journal of the Society for Army Historical Research, 82 (Winter 2004) pp 341–347