Not dun. Dark bay or brown, I'd guess.
Chocolate dun is a bit like cream dun - both terms used when the colour isn't really obvious as anything else!
There is grullo/grulla, which is black + dun, bay dun, brown dun, and red dun (chestnut + dun).
Duns have a dilute body colour (often looks flat and faded) and a dorsal or eel stripe. The stripe is not black - it's a stripe of undiluted colour (so on red dun, the stripe would be chestnut). That occurs in all duns.
They also often have leg barring, darker face mask, lighter colour either side of the mane and tail (think Fjords), shoulder stripes and cobwebbing (thin stripes of colour on the face and forehead) and ventral stripes (similar to dorsal stripe but runs under the belly). They may have none, some or all of these but most will have at least one.
I'd assume that chocolate dun would refer to either black + dun or brown + dun, but I'm not certain.
ETA - if he's Connie, he's definitely not dun. There is no dun in Connies.