The quick answer is that it didn't.
The inboard flaps you refer to are actually split type flaps positioned under the engine tail pipes and not designed to keep flow attached. The mid/outer flaps are 'plain' flaps (no slots or fowler movement).
On plain flaps like those the flow won't remain attached after something like 20-30deg depending on shape and other variables. Modern flaps use slots / multiple segments to encourage flow to stay attached over greater angles.
I've always thought the Comet had pretty large 'barn door flaps'. Perhaps since it's a first generation jet it's engines idled fairly fast and had high residual thrust - which would necessitate large drag flaps for the approach. Just a theory.
...I watched c-beams glitter in the dark by the Tanhauser Gate....