In short, type is used to differentiate one group from the rest and kind is used to link an individual to a group. They are sometimes interchangeable, but not always.
Type refers to clearly distinguishing and essential characteristics or traits shared by members of a group. Its root meaning is "impression."
O+ is the most common blood type in the United States of America.
To mankind in general Macbeth and Lady Macbeth stand out as the supreme type of all that a host and hostess should not be — Max Beerbohm.
Kind, on the other hand, usually refers to a group trait that is shared innately by the members (see "mankind" above). Its root meaning is "race" or "offspring."
The true test of civilization is, not the census, nor the size of the cities, nor the crops, but the kind of man that the country turns out — Ralph Waldo Emerson.
The rule which forbids ending a sentence with a preposition is the kind of nonsense up with which I will not put" — misattributed to Winston Churchill.
She's not that kind/type of person. She is not nasty. She's very nice.
See examples below:
She's not my type. (=I'm attracted to a different kind of girl)
She's not your kind. (=She's a fundamentally different sort of person)
See link1 and link2.