Firstly, I should thank the recent contributors for their remarks about pomegranate juice and gout. So, inspired by the interest shown in pomegranate for uric acid, I checked recent research:
1. Anti-urolithiatic effects of Punica granatum in male rats. N R Rathod et al. Journal of ethnopharmacology, March 2012. Pomegranate juice had a significant uric acid lowering effect in rats.
2. Fruit juice drinks prevent endogenous antioxidant response to high-fat meal ingestion. Cristiana Miglio et al. The British journal of nutrition August 2013. This studies many fruit juices, one of which is pomegranate. It shows that uric acid normally increases in humans, after eating a high-fat meal. However, drinking fruit juices with the meal reduced this rise in uric acid.
3. Benefits of pomegranate (Punica granatum Linn) fruit extracts to weight changes, total protein, and uric acid in white rats (Rattus norvegicus) as an animal model of acute renal failure. Hardany Primarizky et al. Vet World, Nov 2016. Inducing kidney failure in rats raised uric acid levels. But, pomegranate extracts returned uric acid to normal.
Note that none of these studies are real gout studies. So, they do not prove that pomegranate can reduce uric acid in gout patients. But, they do suggest you might like to try.