Can the editor of a book add citations of individual chapters to his own citation count? Supposed someone is the editor of a book, in which individual chapters of the book are contributed by different authors. Other researchers cite individual chapters of the book.

Can the editor of the book add these citations (for the individual chapters) to his own citation count?
No. Generally, an individual's citation count includes only work which they have authored or co-authored.

An editor counting citations of individual chapters of an edited book would be substantially similar to e.g. the editor of a journal adding to her citation count every time an article in the journal is cited. Definitely not an accepted practice.