There is probably no one specific shoe that is good for everyone with gout. There are, however, some design features in particular types of shoes that may be somewhat helpful if you have gout.
Gout is the result of a metabolic issue in which urate crystals get deposited into the joints, most commonly the big toe joint, that can cause an acutely painful arthritis. The main approach to the management of gout is the use of medications to deal with the symptoms and prevent the accumulation of the uric acid and also dietary changes to help with that as well.
Shoes are ‘mechanical’. As gout is a metabolic condition, the prospects of a mechanical interventions helping is not as good as the ‘metabolic’ interventions (ie drugs and diet). Also a lot of the pain in the joint from gout occur at rest, so shoes can not help that.
Having said that, gout most commonly affects the big toe joint of the foot and movement of that joint can be painful and pressure from the shoe on that joint can make the pain worse. This would mean that if the shoes are to help, then they need to have a rigid sole that does not bend much or a rocker sole that the foot ‘rocks’ forward over. Both the rigid sole and/or the rocker design mean that when you are walking, the big toe joint (where the gout commonly causes the pain) does not have to bend so much. This may provide some relief from the pain and make walking easier.
Also, a shoe that has more room in the forefoot in terms of depth and width is less likely to put pressure on that painful big toe joint and also give a little relief from the pain.
While there is no one best shoe that can help gout, there are some design features in shoes (rigid sole, rocker sole, wider/deeper fit) that may be able to give some relief to the symptoms.