A flat was a form of housing on Earth.
During his exile on Earth, the Third Doctor owned a flat in London which Jo Grant had been to. (PROSE: Verdigris) The Eighth Doctor owned a London basement flat for part of the 1950s during his century spent wandering the Earth. (PROSE: Endgame) The Thirteenth Doctor said she'd never had a flat. She was excited about the prospect, suggesting she might buy a purple sofa. (TV: Arachnids in the UK)
Jackie Tyler and her daughter Rose lived at 48 Bucknall House (TV: Love & Monsters) on the Powell Estate. (TV: Aliens of London)
Sometime between 2008 (AUDIO: A Perfect World) and 2020, Thomas Brewster subdivided 107 Baker Street into six flats. (AUDIO: Lost Property) These were occupied at various points by Tania Bell, Ron Winters and Tony Clare, Aisha and Zakia Akhtar, Ken and Robin Bright-Thompson, Liv Chenka, Helen Sinclair, the Eighth Doctor, and the Curator. (AUDIO: Lost Property et al.)
Martha Jones owned a flat during her residency at Royal Hope Hospital. (TV: The Lazarus Experiment) The Saxon Master had a bomb planted in her flat. (TV: The Sound of Drums)
Gwen Cooper and Rhys Williams lived in a flat together. (TV: Everything Changes)
Craig Owens had a flat on Aickman Road. He briefly shared this flat with the Eleventh Doctor. (TV: The Lodger)
Bill Potts and her foster mother Moira lived together in a flat. (TV: The Pilot)
Yasmin Khan lived with her family in flat 34 of Park Hill, a Sheffield council estate. (TV: Arachnids in the UK)
In an fake reality, Panda owned a flat in Bloomsbury. (PROSE: Framed)
Sarah and Brittany Mordley lived in an apartment in Philadelphia in the 2000s. (PROSE: Silver-Tongued Liars)
In an alternate timeline caused by a temporal collision of two versions of the Doctor's TARDIS, the First Doctor, Steven Taylor and Katarina were marooned on the planet Urbinia. As the Doctor worked to repair the TARDIS, the three rented a flat in Kiria City, one that was paid for with Steven's salary. (AUDIO: Daughter of the Gods)