The phrase "a flat place" is correct and usable in written English.
You can use it to describe a location that is level and without significant elevation changes.
Example: "The hikers found a flat place to set up their campsite for the night."
Alternatives: "a level area" or "an even ground".
Because the mission is not interested in rocky terrain or pretty sunsets, planners wanted a flat place with sandy soil.
"I assume it was looking for a flat place to put down, a road or large field".
When Brünnhilde collapses, Wotan lifts her in his arms and carries her to a flat place on the mountaintop: a resigned father putting his daughter to bed.
It is often dismissed as a flat place of endless corn fields, small towns and homely yet conservative values that stretches through the vast interior of the US but scarcely matters to the nation as a whole.
We were not long on the water when Stig turned the Zodiac into the harbor of Hell (in Norwegian, "helle" means a flat place), where another village once stood.
From its opening page, in which he repeats the apocryphal tale of the little old lady who told Bertrand Russell that "the world is really a flat place supported on the back of a giant tortoise", Hawking's intention is to instruct and entertain.
The volumetric flow-rate measurement is done by counting vortices using a flat plate placed in the wake and attached to the beam sensor.
The agricultural world only had a small surplus, leaving the world a very flat place where almost everyone had to remain in tiny, static communities producing that small surplus for the few.
So I'm walking around and around and around and I felt like a hamster and I just wondered why there might not be an alternative since I live in a nice, flat place".
There's a classic, and wrong, idea about Iowa, which is that it's a big, flat place with lots of family-owned cornfields.
A diffuser is a hair dryer attachment that flares at the outside edge, and has a little flat place inside.
