Gout is basically a sign that your kidneys are not filtering well enough to process your diet (at the rate that you eat it). Drinking more water may help especially drinking water apart from meals. Eating slower and smaller meals may help.
Potassium citrate is the potassium buffered salt of citric acid. It's very common naturally as a significant component of pretty much every juice. You might find potassium citrate helps. It actually stimulates and supports kidney function. It helps the kidneys clear more uric acid and calcium from the blood. Citrus juices are good food sources of potassium citrate--especially low sugar lemon & lime juices. (And you probably want to avoid calcium fortified juices.)
Bear in mind that excess potassium citrate will deplete other minerals, so you definitely don't want to overdo it. (Overdoing it can cause porous, brittle bones, teeth and fingernails. Also note that it shouldn't be taken (if taking pure potassium citrate) with food as it hinders digestion (like all minerals).)