He's kidding himself.
He goes into those situations because there's a job that needs doing, and he's the one who can do it. He's afraid not because he's a coward, but because he's not an idiot - but he has courage enough to see it through.
Unfortunately, being A) Victorian and B) British, he's surrounded by people who never, ever, talk about their feelings.So he genuinely believes he's the only person present who finds the situation terrifying, and therefore condemns himself as a coward. His firm belief in his own cowardice then colours his recollection of events - maybe he charged past the Russian guns and into the Cossacks because he was confused, or maybe he did it because he was angry but, in hindsight, can't believe anger could make a coward like him so stupid.
Note that, while brave, Flashman does have a strong sense of self-preservation and is extremely Genre Savvy. As such, he's not going to take stupid risks. Again, his biased recollection colours this good sense as cowardice.
We'll never know the details of Flashman's involvement in the American Civil War. We know he fought on both sides and was praised by both Robert E. Lee and Abraham Lincoln, and claimed that, but for his incompetence, the South would have won at Gettysburg. But there are many mysteries of the war that he might have taken part in, and one is Order 191, the Confederate order found wrapped around cigars by a Union soldier, which led to the Battle of Antietam/Sharpsburg. No one knows how it was lost, but odds are Flashman had something to do with it.
- Wouldn't that be pre-incarnation?
- And McAuslan is the pre-incarnation of Jurgen.