If they're levels are not substantially different, they'll almost always have the same moves. In Kadabra's case, levels can range from 21 - 22, which means that Kadabras at level 21 will have the moves:
However, Kadabras at level 22 learn Miracle Eye. It replaces Kinesis, which means in your case, it will have a different movepool.
EDIT: Since levels are always the same during a chain, the moves remain constant. No move changes will occur.
Hope I helped!