Perhaps preview_chapter() could help you out. Here is an an excerpt from Yihui Xie's book bookdown: Authoring Books and Technical Documents with R Markdown with additional details:
Building the whole book can be slow when the size of the book is big. Two things can affect the speed of building a book: the computation in R code chunks, and the conversion from Markdown to other formats via Pandoc. The former can be improved by enabling caching in knitr using the chunk option cache = TRUE, and there is not much you can do to make the latter faster. However, you can choose to render only one chapter at a time using the function preview_chapter() in bookdown, and usually this will be much faster than rendering the whole book. Only the Rmd files passed to preview_chapter() will be rendered.