Inspirit MultipartURLLoader will probably help. They did not use it for multipart / related, but it has many useful functions for adding files with different types of content.
For example, you can add files with different types of content using the addFile function:
addFile(fileContent:ByteArray, fileName:String, dataField:String = 'Filedata', contentType:String = 'application/octet-stream')
It seems to use multipart / form-data when submitting:
urlRequest.requestHeaders.push( new URLRequestHeader('Content-type', 'multipart/form-data; boundary=' + getBoundary()) );
but you can easily expand it to use multipart / related.
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