Definition problems here. I suspect Flew knows the definitions better than we do. I always thought the agnostic couldn't take a position at all, because he was unable to decide the matter. The atheist comes in two flavors. Flew's kind of "negative atheist" decides that he doesn't believe. That's not the same as saying that there definitely are no gods to believe in. There's the "positive atheist" (using Flew's term, I suppose) who declares that gods do not exist. That's the most extreme position, and quite different from Flew's non-belief. Presumably, Flew is open to the presentation of argument and evidence.
Along the same lines, "agnostic" = "without knowledge" (of a god). Although a word's meaning can change with usage, its meaning is often best taken from the person who coined the term. Here's a nice explaination from AHED:
The term agnostic was fittingly coined by the 19th-century British scientist Thomas H. Huxley, who believed that only material phenomena were objects of exact knowledge. He made up the word from the prefix a-, meaning “without, not,” as in amoral, and the noun Gnostic. Gnostic is related to the Greek word gnosis, “knowledge,” which was used by early Christian writers to mean “higher, esoteric knowledge of spiritual things”; hence, Gnostic referred to those with such knowledge. In coining the term agnostic, Huxley was considering as “Gnostics” a group of his fellow intellectuals —“ists,” as he called them —who had eagerly embraced various doctrines or theories that explained the world to their satisfaction. Because he was a “man without a rag of a label to cover himself with,” Huxley coined the term agnostic for himself, its first published use being in 1870.So, agnosticism is most properly assigned to those who merely admit having no “higher, esoteric knowledge of spiritual things”. It's a weak statement (all atheists are agnostics, but not vica versa), but differs from atheism only for people who can believe in things of which they have no knowledge. Thus the distinction between atheism and agnosticism is dubious.
The distinction is really only useful when communicating with theists. One term elicits more negative emotions from theists than the other term.