Born in 1965 in Heraklion, Crete, Kokkinos gained his first stage experience at the Young Theatre of Crete. He studied dance and theatre at the Cretan Youth Theatre and the Hellenic American Union before studying at the National School of Dance in Athens, where he graduated with distinction. He began his career in Greece. From 1989 to 1992 he was part of the Folkwang Tanzstudio (FTS) under Pina Bausch and performed in pieces by Susanne Linke, Urs Dietrich, Carolyn Carlson and Mark Sieczkarek.
In 1993 he joined the Tanztheater Wuppertal Pina Bausch, where he danced in or assisted with every new piece until 2009, as well as taking on roles in older pieces. From 2002 he was Pina Bausch's assistant and after her death in 2009 he became rehearsal director.
Daphnis Kokkinos has choreographed several notable works, including Addio Addio Amore - a piece for Pina, Lamento for the National Opera School in Athens, The Spring Offering for the National Opera Ballet in Greece, Wandering Dunes for the Šeiko Dance Company in Lithuania, Hug me, it's forbidden for the National School of Dance, and A-mnεmε for the Accademia Nazionale di Danza in Rome.
He has also appeared in films including Talk to her by Pedro Almódovar and PINA by Wim Wenders, and was choreographer for Zenne Dancer. Kokkinos gives workshops all over the world to share his knowledge.
In 2020, Kokkinos was appointed Director of the National School of Dance in Athens.