Does "soul kin" and "kindred spirit" mean the same?
No. Here's the basic idea.
"soul kin" This is not a standard phrase. I think you mean "soul mate". This means that Destiny/Fate/even *** has picked this person to be your romantic partner for life.
"kindred spirit" Someone who has exactly the same opinions an
Soul Kin is not a soul mate. Soul kin are family based upon the soul not by the blood where the souls are born of the same energy. Many times there is no blood relation, no earth bound genealogy. Kindred spirts would be more like a bonded friendship of the soul.