How much clearance is required around a kitchen island?
Ideally, there should be enough room for a person to get by while there is someone standing at the island working.

So enough room for two people to stand side by side across the gap or pass comfortably. If you have to cater for people with mobility problems you will probably need to make this gap wider to accommodate the extra width and lack of flexibility of someone using a wheelchair or walking frame.

However, depending on your design you might be able to get away with less - especially if there's going to be little to no traffic in that area.