Don’t know a great deal about the Blink siren, other than it’s no longer available, but there are a whole bunch of internet based sirens, wireless ones too. If you get one that works with IFTTT, might be available, I haven’t looked, you should be able to make an applet that will trigger on a Blink event. Even if you couldn’t, if the Blink siren had to be manually activated, then you could do exactly the same with any old app controlled siren. The only difference being that you would have to open that app to set it off. Granted a few more seconds, but not too much of a difference between the two methods.
EDIT: Looks like D-link have IFTTT integration, and I’m sure there will be others.