No. You do not lose reputation points for flagging. 

Correctly flagging helps the site and is even encouraged. You start out with 10 flags and you get more flags according to the following rules (from [the help centre][1]):
>When you start out, you are allotted 10 flags per day. This number may increase to up to 100 flags per day:

> - You get one bonus flag per 2000 reputation.
> - You are awarded additional bonus flags when you flag correctly - one bonus flag for every ten net helpful flags (helpful flags minus declined flags).


[1]:https://english.stackexchange.com/help/privileges/flag-posts