If you use the RStudio IDE, you can press the
F7 key or click the menu
Edit -> Check Spelling to spell-check an Rmd document. Real-time spell checking has become available in RStudio v1.3, so you no longer need to manually trigger spell checking with this version or a later version of RStudio.
If you do not use RStudio, the spelling package (Ooms and Hester 2020) has a function
spell_check_files(), which can check the spelling of common document formats, including R Markdown. When spell checking Rmd documents, it will skip code chunks and only check ordinary text.