At present, the echo is not designed to be controlled by other devices. For example, there’s no way to easily have it do a voice notification if, say, the doors are left open. The siren is the same issue. The echo is set up to receive your voice input, parse it with a natural language parser, and then pass along request to other devices. Not to accept incoming requests that aren’t through its voice parser.
You can record individual custom sound as “songs” and then have it play that song, but it’s not very smooth.
You can also temporarily pair it as a Bluetooth speaker to another sound source, like your phone, or your computer, but again, you have to pre-recorded the sound you wanted to play, and you basically lose anything that’s interesting about the echo while it’s acting as a speaker.
You can have a siren sound much more easily from something like a Sonos or any of the cheaper alternatives to that. Or the classic dog barking etc.,
It’s entirely possible that at sometime in the future, echo will have a way to send it “make a sound now” commands, but it’s not in the current command structure.
So there are many different devices and different ways to get different sound to play as alerts when you have a SmartThings system, but echo is not part of that structure at this time.
The fortrezz is a popular networkable siren. And if you’re willing to spend the money, the Sonos is a very popular and very flexible device.