Both kinds of kind come from an Old English word, nice kind from gecynd and type kind from the radically different gecynde. The words are obviously related—gecynd means type or nature and gecynde means natural or native. The gec part of the word disappeared sometime around the thirteenth century, so cynd (with a hard c) morphed into kind. The word kin is alsorelated, coming from the Old English cynn, family.
You can look further back into kind. Before it was gecynd, there was the Proto Germanic gakundjaz, family or race. That word comes from gecynde’s forbearer, gakundiz, native or natural. Gakundiz is a variation of yet another Proto German word, kunjam. It turns out that the ga- is a prefix that indicates the word is applied to a group. Traces of the word can still be found in other Germanic languages; the Dutch kunne (sex, as in gender) is descended from kind, as is the German word for children, kind (like kindergarten). Kunjam is also related to the Proto Indo European word gene, the word that gives us genus.
But that doesn’t tell us how kind went from meaning native or natural in Old English to nice in Modern. The truth is, it just changed definitions. It went from natural to natural feelings to well-disposed to compassionate, all before the fourteenth century. Just because.
TL;DR: Like I said, no reason.
Tony Jebson’s page on the Origins of Old English