The term flat vent has been used for some time to describe a horizontal vent connection to a horizon soil or waste pipe. All vent connections are supposed to be run vertically if possible but there are instances where you may not have any choice but to run a vent horizontally until a wall can be used.
When making a horizontal vent connection a wye fitting is rolled so that it is above the horizontal centerline of the drain, because drains are sized so that there should always be an air space at the top of the pipe. Horizontal vents are installed with a minimum grade of 1/4" per foot(1:50) and should have a cleanout installed where the vent turns vertical.
Sizing a horizontal vent is the same as a vertical vent of the same type. For example if it is serving a single fixture it would be sized as a individual vent.