I have smoke alarms interconnected when power goes off are supposed to beep or not.

I am assuming that your detectors are interconnected to all sound at the same time.
Pushing the test button is not the same electrically as an alarm activation.
The Kiddie manual does not mention the sequence of operations when the test button is pressed. You may want to contact Kiddie to find out if this is ok.
You can also test your detector with smoke to see if they all sound like they are supposed to.

copied from the manual, available at the kidde website

RED AND GREEN LED INDICATORS This smoke alarm features separate red and green LED indicators. The LEDs indicate the following: GREEN LED CONSTANT ON - AC power is present. OFF - AC power is not present. RED LED - Can be seen through the Push-to-Test button. Blinks once a minute - Indicating presence of a working battery. Blinks once a second - Smoke alarm senses smoke and simultaneously sounds an audible alarm. Blinks once every 10 seconds - Smoke alarm is quieting an unwanted alarm (Model ADC only). (Interconnected system only): OFF - Another smoke alarm in the network has sensed smoke and is signalling this alarm.

According to the Kidde website, model KN-COSM-B-RF can interconnect with "Up to 24 devices (of which 12 can be smoke alarms)", so I would say the answer is "yes". The Kidde website also offers a place where you can submit questions...I'm sure they would be happy to help you. Kidde KN COSM RF Battery Operated Wireless Interconnect Combination CO and...

Sorry but I was misinformed and gave the wrong information and I am taking it off.

If you wire fire alarms together you may not have the coverage you should have. If you have a fire alarm in one part of a house and put another one hooked to it then if a fire puts the power out in that part of the house then you have no protection in the other part if it's on the same circuit. There has to be a different circuit for each alarm.

Black is hot. White is ground. Red is interconnect.

No,this thing a smoke alarm detectors,damp air doesn't set it off.

I would pose this question directly to the manufacturer. I'm kind of surprised that the AHJ would approve such a configuration to begin with, as I would not have thought such interconnection would meet the intent of the code for notification, but then I don't know all the circumstances. I would ask Kidde directly.

it could be a parallel wire, connecting the smoke detectors to each other so that if one goes off they all go off, do the other smoke detectors have the same wire ?

Your alarms are interconnected, meaning when one alarm goes off, they all go off. The alarm with the flashing green light is the one that triggered the alarm. If it only went off once, it was probably just fluke thing, and you can reset the alarm memory (flashing green light) by pressing the test button. If it happened more than once, you should try cleaning the alarm. Do this by removing the alarm, and blowing compressed air into the sensor opening (located around the back side perimeter of the alarm). If this fails, replace it.