Visual Studio Code – How can I paste images into my markdown files in VS Code?

First you need to enable editor.experimental.pasteActions.enabled ("Enable/disable running edits from extensions on paste."). Then you can set markdown.experimental.copyFiles.destination configuration according to its documentation:

Defines where files copied into a Markdown document should be created. This is a map from globs that match on the Markdown document to destinations.

The destinations may use the following variables:

• ${documentFileName} — The full filename of the Markdown document, for example readme.md.
• ${documentBaseName} — The basename of Markdown document, for example readme.
• ${documentExtName} — The extension of the Markdown document, for example md.
• ${documentDirName} — The name of the Markdown document’s parent directory.
• ${documentWorkspaceFolder} — The workspace folder for the Markdown document, for examples, /Users/me/myProject. This is the same as ${documentDirName} if the file is not part of in a workspace.
• ${fileName} — The file name of the dropped file, for example image.png.

For example, to paste any pasted images in the same directory as the markdown file you are pasting into, use:

"markdown.experimental.copyFiles.destination": {
    "**/*": "${documentDirName}/"
}