Does turmeric relieve gout pain? The most likely answer is no. It's not even turmeric that was tested, it was curcumin in the two studies most often quoted, and the second study was another "extraction" from curcumin.
The Elephant in the room? We would better make that plural because there are more than one in the room.
Curcumin only accounts for 3% of Turmeric. If you consumed enough turmeric to make a difference, over time you would likely die from malnutrition for lack of a variety of vitamins and minerals. An adult would have to eat a lot of it several times a day, and it would be counter-productive.
In both of the better studies, not one account of anything else in their diets. Poor controls.
Don't lose hope!
Here's a solution, find a quality curcumin supplement and not modify your life more than you must. Even though I think they had poor controls in place, it likely does have stout anti-inflammatory properties with a consistent dosage, and it's natural.
Although this is the short story of Turmeric and gout, it would be better to spread the word that Turmeric has plenty of other benefits, but helping a gout attack is likely not going to happen. I ran across a post on a site that has a more detailed post about turmeric and gout called ExitConfessions that will give you more insight than my post here.