Firefighters using breathing apparatus evacuated the 14-storey building in Millmead Road, Margate, after the fire started at 0840 BST on Thursday.
One person, who was rescued from the 12th floor, was treated at hospital for the effects of inhaling smoke.
About 50 firefighters tackled the fire which caused damage to two storeys at Invicta House. Residents were allowed back into their flats two hours later.
One evacuee said: "I thought it was fog at first.
"I went round a door and got a big blast of hot, black smoke, right in me mush."
Nick Keech, of South East Coast Ambulance Service, said: "All the emergency services worked extremely well together in what could have been a much more serious incident."
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