1 Bluetooth speaker can be manually disconnected and forgotten and then be put into pairing mode again. You "must" forget the pairing because the Bluetooth core spec prioritizes the pair. This means it will immediately connect to the 1st pair option detected. You can work around this by turning things off and then back on but that can be challenging. What I mean by this is if you have 1 BT speaker paired with your computer and a Dot (or substitute your multiple devices) you can turn off the device(s) you don't want connected, allow the speaker to connected with the currently-powered-on-device, and then power up the other devices which will be ignored by your speaker because it is already connected.
I have never searched for a BT speaker that supports multiple connections (meaning it internally has multiple BT radios) so cannot comment.
Additionally, I am guessing what you would like is 2 Amazon devices connected to 1 BT speaker and audio from both devices played over that speaker. Ignoring the concerns regarding overlap (meaning what if both stream something or respond to a command) what you need is a "receiver".
"Receiver", IMHO, is the stupidest term in audio because there's no clear definition and you can't search on it (and successfully find what you need unless your need is ridiculously generic). You need a Receiver that will support multiple BT audio channels and then provide mux (multiplexing) across channels. Complete lack of consumer demand means you probably won't find this solution but I can provide a helpful pointer that begins to address your need:
https://www.soundandvision.com/content/how-origin-making-beautiful-music-amazon[edit]One additional point: Each Amazon device (AFAIK) comes with a standard 1/8" audio stereo jack audio output. These can be run to an audio receiver with multiple inputs and do what you want. You will either have to select which input the receiver uses or find a receiver that allows for muxing, auto-switching, or other features you may require. Once you have the receiver it's fairly easy to find common cables of the type you will require (e.g. 1/8" stereo jack to stereo RCA).