If you want to do it across a batch of files you can use Actions in Mp3tag to achieve this ('Export cover to file'), although it looks like you'd need to setup one action per artwork type (Front, CD, Artist, Back e.t.c.) just so that you can name them correctly. You can have multiple Actions per Action group though so you'll only need to run it once.
The only other way I can think of achieving this is by scripting metaflac.
This lists all the artwork types in a file
Code:
$ metaflac --list --block-type=PICTURE 01.01.flac | grep -A5 -i metadata
METADATA block *3
type: 6 (PICTURE)
is last: false
length: 162685
type: 3 (Cover (front))
MIME type: image/jpeg
--
METADATA block *4
type: 6 (PICTURE)
is last: false
length: 148453
type: 4 (Cover (back))
MIME type: image/jpeg
--
METADATA block *5
type: 6 (PICTURE)
is last: false
length: 77788
type: 8 (Artist/performer)
MIME type: image/jpeg
--
METADATA block *6
type: 6 (PICTURE)
is last: true
length: 159205
type: 6 (Media (e.g. label side of CD))
MIME type: image/jpeg