I agree with tepatria. As used in the sentence both light and bright will be taken to mean light or bright in colour, rather than well-lit. Light could also mean light in weight. A flat being light in weight doesn't make much sense, but nevertheless the phrasing gives the impression that this is what is meant.
Bright, in reference to an interior, however, may also refer to its ambience, which may be a combination of colour and lighting. It still does not give the impression to me that it only means receiving a lot of light, though.
I agree with MM that a "bright flat" doesn't necessarily mean that it's light. It could be painted with gay colours that make it "bright". If I wanted to describe such a flat, I'd probably say "light and bright" or "light and sunny".