Chocolate dun is one of those wierd terms that you won't actually find a definite definition of
I think what most people would describe as chocolate dun would be seal brown or dark bay with dun.
So; first step is to work out whether either of your mare's parents were dun. If neither were dun, then your mare is definitely not dun.
If at least one parent is dun, then you need to look at your mare and see if she shows any factors associated with dun.
Duns *always* have at least diluted body colour (the colour will be diluted to a flat, muted shade) and a dorsal stripe. This is where is starts to get slightly more complicated...
Dorsal striping on a true dun is different to teh stripes you get on non-duns. This is Tia, my liver chestnut mare (and yes, I know this pic makes her look bay. She has a bright ginger winter coat adn very dark points, but she really is liver chestnut) showing her 'dorsal stripe'. It looks like what most people would class as a dorsal stripe (bearing in mind this is winter coat and pretty furry) but it is not a true dorsal stripe for a couple of reasons.
Note first off how the edges are not pin-sharp. On a dun, they would be. The colour 'runs' from the stripe into the body colour - on a dun, that wouldn't happen.
Next, if you look closely, you can see that even though the stripe runs down into the head of the tail, it doesn't conitnue down the dock - on a dun, it would.
The body colour is not diluted. That's the most obvious giveaway.
The hair at the top of Tia's tail is not diluted or frosted - on a dun, there will be lighter, grey or silvery hair at the tope of the tail.
Tia's stripe only appears on her winter coat. Her summer coat is so dark this is hidden; on a dun, that wouldn't happen. Stripes, masks, shoulder and leg barring are all clearly visible all year round, and not subject to changing with coat changes or sun-fade.
Striping on a dun is the same colour as undiluted body colour. Imagine it like this; dun dilutes the coat colour as sunlight fades fabric. If you cover parts of the fabric up, the sun doesn't fade it - so you get patches or stripes of the original, unfaded colour. Dun striping is a bit like that; stripes of undiluted base colour. Countershading, like Tia's stripe is in reality, is caused by the addition of darker hair, so will appear darker than the base colour.
Ok, so that's striping covered...
Duns usually have other characteristics too; their legs are often darker but mane and tail (even black manes and tails) will usually be diluted to a greater extent. Black pigment is diluted as well as red; on a horse with black legs, although the legs won't be diluted to the same extent as the body, they won't be undiluted black.
They will usually have streaks of lighter hair on the outside edge of mane and tail, and often have pale hair inside the ears or on the ear tips.
They often have leg barring - again, this is base colour and does not alter or fade with the seasons.
They can also have wither stripes, dark markings on the shoulder, and cobwebbing on the face.
Just about every dun factor marking is immitated by 'countershading' in the absence of the dun gene; horses with primitive markings or countershading can do an incredibly good job of mimicking dun markings. But there are differences, and you can usually tell them apart through looking closely and watching for changes over a season even when they are very convincing!