Flintoff is most certainly a bowling-all-rounder, in Tests, in my book (genuine all-rounder in ODIs). Distinct from a bowler who bats a bit, like Swann, but not an out-and-out all-rounder.
I've heard people go through the "can contribute to the game with bat and ball" thing before - think Fuller was one of the most vocal - but I've never agreed with that. Ricky Ponting can contribute to the game with the ball, he just hardly ever does; James Anderson can contribute to the game with the bat, but he's still no more than a very good number-ten. Certainly, neither are all-rounders nor close to it; Ponting is a batsman who occasionally bowls; Anderson is a bowler who bats a little bit. Swann is a bowler who bats a bit. Even Mark Ealham, who's a considerably better batsman than Swann, was no more than a bowler who bats a bit at the top level.
For me, there's:
batsman
batsman who bowls a little bit
batsman who bowls a bit
batting-all-rounder
all-rounder
bowling-all-rounder
bowler who bats a bit
bowler who bats a little bit
bowler
All of whom can be anywhere on a scale of outstanding to poor.
No need for all this over-sanitised three-stage-only stuff. It's semantics, but so is "cricket player" or "baseball player". It's a question of what you define things as.