The phrase "a sort of flat" is correct and usable in written English.
It can be used to describe something that is somewhat flat or has a flat quality, often in a figurative sense.
Example: "The painting had a sort of flat quality that made it less engaging than the others in the gallery."
Alternatives: "a kind of flat" or "a type of flat".
The result was Plus Minus, a score which provides some basic musical material, and then much more elaborate instructions for turning that material into a finished piece – a sort of flat-pack composition.
The fighters took me through an archway and up a flight of stone stairs to a sort of flat-roofed ruin overlooked by Jebel Mohsen.
The idea of a sort of flat-bed platform to stand in for a train is especially misguided but that's just one of many touches, like the would-be iconic jumble of chairs or the simple wooden desk that remains on stage most of the night and seems to be sat at by just about every character at one point or another.
Paper, but magnetic, they are designed to cling to a sort of intelligent flat screen-cum-notice board in your kitchen.
"She used to live in a sort of horrible flat -- though it was in the 16th arrondissement -- but she seemed to be hardly getting by.
After decades of working the audience, Jacobi seems to have become all face: his head is a sort of large, flat professional mask that well suits the King, whose last great show of authority is the ceremonial handing over of his land, his cares of state, and his best-loved, youngest daughter, Cordelia (Pippa Bennett-Warner), in marriage.
The clock is positioned fifteen feet above commuters' heads, right at the point where the new entrance and the old concourse intersect, and at first glance it looks nothing at all like a clock, but like a sort of modern-day flat, ceiling-mounted sundial.
A sort of mesa rose, flat-topped and alone, out of the middle of a field.
While there is something new and strange in Nordic noir, the genre is also reassuringly familiar: the dyspeptic, whisky-guzzling Swedish cop Wallander is a sort of Baltic Inspector Rebus; the flat, monotonous landscapes of the Danish TV crime epic, The Killing, could almost be those of Norfolk.
