Bicycles/Maintenance and Repair/Brakes/Coaster Brakes
Coaster brakes don't need adjusting but they may need lubricating to reduce wear. They are supposed to be greased with a special high viscosity lubricant such as Sachs: "fett fur stahlbremsmantel" which is likely no longer available. So instead use a cheap, high friction grease. To take the hub apart, Torpedo and Sturmey Archer say to start on the brake lever side, but I've seen the opposite proposed.
However, you need to take apart the hub to apply grease so it's a lot easier to lubricate the brakes with heavy oil that doesn't contain anti-friction additives. Apply it via an oil filler hole in the hub (if it exists). Don't use oil with anti-friction additives such as teflon or graphite that will result in slippery brakes.
On a long downgrade of over 1000 feet (300 M) the coaster brake may overheat and the any oil in it may boil and smoke. One may try filling the hub with water to keep the brakes cool by generating steam. Make sure that all the water has boiled off by the end of your trip. Do not expect a coaster brake to perform reliably or safely in hilly terrain. It's even possible to melt metal inside the hub. Also realize that if your chain derails or breaks, your coaster brake will no longer function.