Most simple way without running anything else, see VoiceMonkey.io. Need to do things in multiple places but fairly easy once you understand it.
You'll create a device there, then link voicemonkey to your Alexa account, add the device to Alexa in the app, then in BI under Alerts > Actions > On alert you'll add a line for a web request that looks something like this:
I do this through Home Assistant with the HACS Alexa Media Player integration. I don't know if this integration can be standalone for Blue Iris though.