How can one define 'secularist bigot'?
A secularist is someone who advocates church/state separation with the strong conviction that the separation should not be softened or ignored for specific cases.
A secularist bigot would declare secularism immune from criticism.
Richard Dawkins is clearly not the latter, he does dicuss arguments, and allows completely free discussions on his own internet page. He's just not convinced by flowery language aimed at ceding privileges to religious ideals. Anything of that sort would be allowing stealthy theocratization of the state.
Flew seems to have lost the ability to discern the difference between secularism and extreme laicism or enforced atheism, or the ability to understand simple arguments (assuming he had read them which he obviously didn't). This would be a failing ground even for a beginning student.
Sad.