I searched a lot and could not find a syntax-aware spell check for Markdown. This means it would ignore things within backticks, code blocks, URLs.
The most serious discussion is at Atom, specifically this Atom spell-check issue. It references several other issues that were consolidated into that one.
This is a major deficiency of the Markdown ecosystem.
I’m wanting to recommend coworkers write most things in Markdown, but only if it has spell checking.
When you use regular spell check on a Markdown file, there is too much noise. You have to ignore or add every single variable name or part of a file path or language keyword. It’s unusable. It needs to be syntax aware.
And one more general request to the universe: that people write their general tools like spell checkers as libraries/programs that could be used within the most other tools. Too much Markdown syntax aware tooling is locked behind specific editor plugin code. Way too much repetition of such a common need.