BigTalker (when in musicPlayer mode) currently only sends desired text phrases to SmartThings to be converted to audio. The result is a URL to an mp3 of the phrase you wish to speak that is then sent to your musicPlayer device and played. There is not currently an option for playing a custom hosted or local mp3. It’s an option that I have thought about in the past but not implemented.
When BigTalker is in speechSynthesis mode, the text phrase is sent to your speechSynthesis device and it converts it locally to spoken audio. You might be able to accomplish what you are wanting if your device is an Android and if you install and configure LANNouncer.