Mixing the light upholstered chairs with the darker slate captain's chairs creates contrast and gives the dining room a more interesting, collected look. The dark wood frames connect the two chair styles, while the lighter upholstery keeps the space from feeling too heavy.
I know you mentioned green for the captain's chairs, but the room already has a lot of green with the walls and the rug you selected. The slate adds much-needed depth, helps ground the lighter wood table, and ties in beautifully with the blues and grays in the rug and artwork.