I have a set of small walkie talkie radios with a charger base. Each radio require 4 AAA batteries.
Power supply is marked 7.2v. When I check the charge port it reads 14.3v. Is this normal or is my power supply whacked?

Do you mean the AC adapter says it is supposed to put out 7.2V and when you measure it (not connected to anything), it puts out 14.3V?

That isn't necessarily abnormal. Cheap wall-wart power supplies often put out higher-than-normal voltages when there is no load (no current draw). The voltage drops to approximately the rated voltage once power is actually being drawn.

There isn't a great way to test if that adapter works that way without having a dummy load of approximately the correct resistance. Shorting it would drop the voltage but could damage the adapter.

Higher no load voltage is common with some chargers. I have a couple of Solar battery chargers that put out a measured 22 Volts in direct sunlight but work fine on 12 Volt motorcycle batteries.