Ok, I was still trying to answer the original question you had, and not the later question about dx tool failing.
It seems to be a known issue, that Adobe are trying to fix. Look at this discussion:
AIR25 - dx tool failed
and at messages 12 and 13. It's saying that the known problem is to do with the latest Java update, and message 13 gives a link for you to be able to download and install the previous version of Java.
In an attempt to avoid messing with Java, I installed AIR 24.0.0.180 in Flash CS6 and my apk was created successfully.
I then uploaded it to Google Play and I immediately received an email of rejection for the same reasons.
However, that must have been a software glitch because 44 minutes later I received an email announcing that my app was live in the store. Go figure . . .
Many thanks to kglad and Colin Holgate for leading me to this solution!