Are there any sources that can confirm or deny if they were kinsmen (family, not race)? After all, they both lived in Doriath and were similar in appearance.
There's nothing to explicitly confirm or deny it. The only thing we know about Thranduil's parentage is that his father was a Sindarin elf of Doriath, named Oropher:
[A]t last Thranduil established his realm in the north-east of the forest and delved there a fortress and great halls underground. Oropher was of Sindarin origin, and no doubt Thranduil his son was following the example of King Thingol long before, in Doriath; [...] [T]hey (and other similar adventurers forgotten in the legends or only briefly named) came from Doriath after its ruin and had no desire to leave Middle-earth
Unfinished Tales Part 2: "The Second Age" Appendix B: "The Sindarin Princes of the Silvan Elves
But we know nothing about Oropher's familial connections.
All we know about Thingol is that he had two (known) brothers:
- Olwë, who went to Aman and became King of the Teleri
- Elmo, grandfather of Celeborn in some of Tolkien's later writings
There is no known connection between the two families, but any number of possible ways you could imagine one occurring.