How do I refinish a kitchen island from dark oak to distressed white

Chalk paint would be a good option for this project. You can do one coat and then sand and distress or add a second coat before you sand and distress. Finish with chalk paint wax or clear sealer.

After a good cleaning I would use a good sealer like Kilz before painting.

Could try White Chalk paint - Distress - Seal with Clear or Antique Wax.

Try chalk paint!

Sand and prime with Kilz - then paint with latex paint that is washable.

You might consider chalk painting it white then sand it a little to distress it. That would be beautiful

Rustoleum Cabinet Transformations

Here are before and after using the Cabinet Transformations.

No you do not need to prime before using chalk paint. If your island has a glossy finish--from poly--I would sand lightly just to knock down the gloss before I used chalk paint. Keep in mind that some less expensive chalk paints don't seem to adhere as well. I like Annie Sloan and Country Chic for projects like an island. Rustoleum Chalked Paint works OK--it is less expensive--but I don't think it works as well on this kind of project. I like it for smaller projects like signs and trays, etc. Country Chic has a little bit different way of distressing so I would go to their website and watch the videos. And for Annie Sloan--you do not have to buy their expensive brushes--I just use a good brush--Purdy is an example. And be careful about only brushing the paint on in one direction--not back and forth. I thnk for the island I would go with the Annie Sloan. And if you are new to chalk paint--watch some videos.