I think this is because you are using relative path.The markdown syntax for image insertion will be translated to HTML with a relative link and I guess your image is not in the same place relatively to the HTML page of your post. You can have a look at the HTML source code to see the path used in the HTML to the image, and you may see why it is not found.
Can you try embedding the image using knitr::include_graphics() ? Not sure it take care of that but that worth a try.
You can also use an absolute path, but it will work locally but not when you published I think.
Usually, it is better to have images located at the same location than your Rmd post. It is the same with any supporting files you may have for a post. This will insure that those supporting files are correctly moved to the website: https://rstudio.github.io/distill/blog.html#supporting-files
I let other with Blog experience with distill to share there experience. @tom_rstudio do you have some advice on how to better handle images with distill blog post ?
Hope it helps.