Kind refers to substances that have the same properties and are very similar, and can be classified as one category.

What kind of cake do you like best? What kind of cake do you like best?

sort can be used interchangeably with kind, but it is rather vague, and sometimes it only means something like this. Sort sometimes has a contemptuous meaning, while kind is much more solemn.

He makes friends with all sorts of people.

Type refers to type, type, which is more specific, certain, etc., while kind is more general and vague.

Men of his type are not to be trusted. People of his type are not trustworthy