Complex sentence: Flint resigned after the Cabinet reshuffle of 5 June 2009 asserting that Gordon Brown was running a "two-tier government", and believed that she had been treated as "female window dressing".
Split into simpler sentences: Flint resigned after the Cabinet reshuffle of 5 June 2009. She resigned claiming that Gordon Brown was running a "two-tier government", and that she felt she had been treated as "female window dressing".