"rent a flat" is correct and usable in written English.
You could use it in a sentence like this: "I'm moving soon and need to rent a flat in the city."
Lines would include: "One does not simply rent a flat in London for less than £1,000 a month"; "One does not simply get a job in the current economic climate"; and "One does not simply get an operation on an overburdened NHS without waiting about a year, sometimes more".
"We're going to rent a flat together".
I now rent a flat in my new city.
It's about a group of students who rent a flat.
Besnik worked in a pizzeria to make enough money to rent a flat.
If you have no right to be here, you cannot rent a flat or a house.
"He's never had to rent a flat - his parents bought him one when he was 18.
In Bolivia, 500Bs per month is enough to rent a flat.
The new plan is to rent a flat in zone one for five people.
We rent a flat, it's the cheapest way to hunker down, get yourself a dunny.
Some friends and I will be going to the same university, so we want to rent a flat together.
