Authenticity of every Hadeeth comes through thorough study of high caliber of Ulama who have long experience in the knowledge of Hadeeth and Rijaal
( narrators). Al-Kaafi is one of of our four most authentic books of Hadeeth. We do not claim in Al-Kaafi what our Sunni brothers claim in Bukhari book that everything in it is authentic. We believe that Al-Kaafi has thousands of authentic Hadeeths and our scholars are always free to research in every Hadeeth. When the scholars find a Hadeeth is authentic after studying all its narrators and the context, then it is authentic.
Our leading scholars who researched every Hadeeth in Al-Kaafi say that out of over 16000 Hadeeths in this book, at least 15000 Hadeeths are authentic.
You need to refer to the Marji' of Taqleed for final judgment in any Islamic rule.