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This goes to show how poorly information about skills is made available. There is a skill that does this:
It seems like a no-brainer, and is a problem I worked on (to play iTunes music and watch Kodi movies as well as control your computer) and found a solution, but Amazon would not approve my skill, claiming it promotes piracy. I am assuming this is in reference to Kodi support, which was only selected because it can be scripted (and thereby controlled).
I am not associated with these guys at all. But, it is inexpensive. This does not access your iTunes in the cloud, so you need your MP3's (in non protected format) on your computer, which it will then stream to your Echo. It doesn't even need iTunes.
That capability that I mention (turning a Bluetooth source into a streaming source) is not actually a direct, inherent function/feature of My Media but is something that can be accomplished using My Media and another free tool using a computer as a server.
My Media for Alexa is a program/software/Alexa Skill that allows you to listen to your own local media files (mp3's for example) on your Amazon Echo devices. Basically you install a small program onto a computer on your local network, in your home. This program creates a small local web server and an interface/console (picture) that you can access from any computer/tablet/smart phone on your local network. Think of it kind of like iTunes except it plays the music back on your Echo devices after you request Alexa to "open 'My Media' and play X song/album/playlist/etc.'" (picture).
By default it will only play on one device at a time, however, there is a trick where you can use Alexa's/the Echo's "preferred speaker"/ feature in combination with adding each of your Echo Devices into a device group in the Alexa App which then will play streaming audio from one particular Echo device onto however many other Echo devices you would like in unison/at the same time (picture). It's kind of confusing to explain and don't bother asking any Amazon Echo Customer Service person about this feature because they will be totally confused and have no idea what you are talking about. You don't actually go into the Alexa App and create a multi-room-music group but it actually does create a multi-room-music group on the back-end/it doesn't show in your local list of multi-room-music groups that are shown in your Alexa App under 'Devices' --> 'Echo Devices' but it is there and shows in your list of multi-room-music groups on Amazon's end/the Customer Service rep. sees it as one of your multi-room-music groups on their end. Basically, it's poorly designed and implemented by Amazon (like much of their everything is) and their staff is poorly trained/isn't at all trained on how this feature works, but it does work! Here is how My Media explains how to set this up on their website.
So, getting back to streaming Bluetooth "live" to your multiple Echo devices... one additional feature of My Media for Alexa is the ability to create a playlist item that you can ask Alexa to "open My Media and play" which is actually not a local .mp3 file on your server but is a web streamed/"live" mp3 file. It's kind of a hidden feature. Anyway, using this feature in combination with one of a number of available free tools to live stream audio from your computer to a local mp3 file (such as Stream What You Hear on Widows, Broadcast Using this Tool 'BUTT' on Linux, etc.) you can have My Media play this "live" local .mp3 file that you computer is streaming (picture). This is how you could play a Bluetooth-streamed device that you have connected to your computer to Alexa, using the aforementioned tools/process. You can stream anything though (a line-in/aux cable from a turntable, your computer's local audio, etc. for example) - doesn't just have to be a Bluetooth device.
There is also the mymedia skill, which is similar to the Plex skill but only for music: https://www.amazon.com/bizmodeller-My-Media/dp/B06XPP135L
I don't know if using that skill will give you any different behavior though
Alexa apparently has skills: https://www.amazon.com/bizmodeller-My-Media/dp/B06XPP135L/ref=sr_1_25?dchild=1&qid=1613384155&s=digital-skills&sr=1-25
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Do some research there. There is probably a DLNA server or something that can help you with this.