Given the fact that when you key up the mic you should not hear any thing because the receiver section is "turned off" (no antenna and the speaker is muted). This would seem to indicate that the switch the headset controls which allow the change over from RX to Tx is bad or that the circuit in the CB unit which the head set plugs into is having a problem. Do you hear the same flutter without the headset? Try to get another headset or test one out just to see if the problem is eliminated by using a known good headset.
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