No, I have not info on his relatives. There are more than 1500 adresses of Klingenberg today in Germany.
You can read on www-sites (like you have shown) or in books. Example for books (in german language):
Ernst-Günther Krätschmer; Die Ritterkreuzträger der Waffen-SS; Verlag Nation Europa, Coburg; 4.ergänzte Auflage 1999, ? ISBN 3-920677-43-9; (Knight´s cross holders of the Waffen-SS; pages 137 write about Fritz Klingenberg)
Fritz Klingenberg was born December 17th, 1912 in Roevershagen county Mecklenburg (northern-Germany near town Rostock), killed March 22nd, 1945 near Herxheim county Pfalz (south-west-Germany near town Karlsruhe).