The use of alkaline water to help gout has been raised many times, and I will summarize old discussions here.
There are two aspects to consider.
First, the act of taking on fluids is almost always a good thing for gout sufferers, within reason. As most drinks contain an extremely high proportion of water, it does not matter what the drink is. Avoiding dehydration allows the kidneys to excrete uric acid better, but there is little benefit beyond that. Most important aspect is to keep urine output to around 2-2.5 liters per day which helps avoid kidney stones. This is also true when on allopurinol, because unused allopurinol, usually excreted as oxypurinol, can form stones in extreme cases. For more, see my articles about water and gout.
Second, is the issue of alkaline water “dissolving” uric acid. There is no evidence to support this claim. There is evidence to suggest that alkaline urine helps to lower uric acid. It falls into the category of “more research needed.” Even if it is true, you should not believe marketing statements that push alkaline water. Our body chemistry is complex, and alkaline intake at one end does not necessarily cause alkaline output at the other end. There is much more about this in my alkalizing gout diet menu articles.
One thing is certain. If you are trying to alkalize your body, which I personally recommend, you must test the pH of your urine.