If you have gout, you need not avoid eating avocados because doing so will not exacerbate the painful symptoms of gout.
Gout is caused by excessive protein (especially animal protein) and alcohol intake. Avocados are very low in protein as only about 3% of their total caloric composition comes from protein.
85% of the calories in avocado comes from fat, mostly monounsaturated fat, about 16% is carbohydrates and fiber, and the remainder is protein.
So, rest assured that eating avocados is good for gout. In order to reduce your symptoms, you should try to get the bulk of your diet from plant-based sources and avoid meat and alcohol.