How to add class to field--item element generated by paragraphs
It depends a little on how your Paragraph is structured. Is it a single paragraph type with multiple generic fields in it or a paragraph with multiple other paragraph types inside of it? 

If it's the latter, you have to create two twig files (For the parent and the child) but you can control output for each row and the contents of each row.

Alternatively, if you are just trying to style each item what's wrong with just selecting the field--item elements, eg:

 .field--whatever-parent-is-called .field--item { style here. }