The baro damper can be placed on either a vertical or a horizontal pipe. As Cap says, it looks like there is room for it on the horizontal run between the upper elbow and the chimney.
The baro won't increase draft, it will reduce it to the proper level if you have too much draft. Your chimney looks like it has adequate height to provide good draft. The only worry might be, because it is exposed to cold outside air, at low stove outputs the flue gases might be chilled too much to maintain the draft.
This advise is right on the money.
We live on top of a hill and sometimes the wind comes rushing up with some gusto, i'm not sure how that influences my situation.
Wind can drastically increase your draft. A baro damper will compensate for this but I would wait till you're burning only coal before installing the baro because the baro will cool the chimney and cause creosote to build more quickly. Because the chimney is on the exterior of the house it will be cooler and more prone to creosote build up as well.
One more thing, and I don't mean to preach, but I would move the fire wood away from the stove just to be safe. You don't want a spark to pop out into the wood pile.