Short-range (10') AM-band transmit from 3.5mm Android headphone jack

Yes that circuit is basically correct although you don’t draw connections going into a capacitor like that. Just have one wire out of the capacitor and connecting to the other components. However the capacitor needs to be a lot bigger something like 47uF.

Now if you read the analogue input with no audio you will get a reading around 512 and with audio it will be above and below this. If you don’t get that then you have something wrong or the Audio from your phone is not loud enough.