The phrase "flat side" refers to the side or surface of an object that does not have any curves or bumps. It means that the surface is smooth and even, like a flat table or a straight line. Full definition
Apply cream gently to middle of stain with flat side of apparatus in the box. (skincareof.com)
A classic, low - profile sofa with flat sides and back preserves the visual flow between spaces, but its strong, square outline can define a seating area. (idealhome.co.uk)
To do this, lay cabbage flat side down on the board and cut a «v» in the centre. (changs.com)