'Shooting flat' is a filmmaking term for shooting without any settings baked in. This is called RAW when taking stills. Normally when you take a photo the colour balance, colour settings (saturation etc), and ISO - basically all the digital modifications are baked into the photo, meaning once its taken, you cant change it. While you can use post to make changes after, you are very limited because its digitally imposing on the baked video/photo you took. When shooting Flat/RAW, the camera catches much more of the data, and gives you a RAW file (not a compress file like JPG, MOV). This allows you in post to change the digital effects (like colour balance, ISO etc) to the original image without effecting the quality of the video/photo.
Should you shoot flat? It really depends.
The first thing to consider is do you need to? If you are going to be colouring the video/stills, then this is something you should do. If you are taking short clips to add to FB, maybe don't bother, because if you shoot flat, you need to colour correct, which is time consuming.
Secondly, flat file formats are big in size (think 5+ times the size), so you need to be prepared for that. If you dont have a lot of cards and plan to shoot lots of footage, maybe don't do it.
It really depends on the project
