If this is a Chrome OS app, you can use the
accessibilityFeatures API and that will tell you if ChromeVox is running or not.
If this is a Chrome app for platforms other than Chrome OS and you're sure you only care about ChromeVox and not other assistive technology, you can use the
management API to see if ChromeVox is running by checking for its ID.
If this is a web app, or if you want to support other assistive technology other than ChromeVox, then there isn't a way to determine if a screen reader or other similar tool is running. If you want to control what's spoken and not interrupt existing screen reader speech, you could use ARIA live regions, but I'm not aware of a solution for audio, sorry.
If you have more questions about ChromeVox in particular, you can use the
chromevox-discuss group.
Hope that helps,
- Dominic