A Flat Trans (short for Flat Transportation) is a transporter that is described as being a "shimmering wall of grey". The Gladers use one at the start of The Scorch Trials to enter the tunnel under the Scorch, and later find out that they are extremely expensive, which is why no one believes their story of how they got in the Scorch.
All of the immunes use a Flat Trans at the end of The Death Cure to escape the WICKED headquarters into a place they call paradise, for it is the last place on Earth that hasn't been destroyed by the Sun Flares or the Cranks.
A Flat Trans is also referenced in The Kill Order several times and, at the end of the book, a Flat Trans is what the PFC scientists as well as Deedee escape from Asheville in. Upon walking through the Flat Trans, the feeling is described as a cold line running across your body as you step through.
It is revealed that the flat trans can be controlled when Brenda makes it disappear from existence using a control panel next to it in The Death Cure.