As you know Kentucky remained loyal to the United States and never joined the Confederacy. That means the state was spared most of the economic horrors of re-construction. The distilling industry was like any other business in Kentucky and had to deal with damages of 4 years of bushwacking by forces loyal to either side and a couple of major battles. Farms were damaged and the slave labor was now free. It took some time to get crops in and roads safe to travel, but by the end of 1866 things were getting back to normal.
As Chuck said, the distilleries sold to both sides of the war and for the most part avoided destruction at the hands of bushwackers and raiders. They did have to deal with a new tax that was not going away and registration of their warehouses. By the end of the decade there are a lot of distilleries that are expanding and other new companies being formed. Compared to other southern industries, the distilleries did all right.