If your CLT-JFK flight is ontime, you'll have no problem making this connection. When leaving JFK, do not go to the baggage claim area. Instead, exit the door on the departures level that is directly to the right of the security area. (You'll walk right past it on the way to the baggage claim area. The door is between the security area and the escalators that go down to baggage claim.) Then walk straight ahead to the front of the terminal, where you'll see a separate down escalator that will take you to a corridor that leads to the AirTrain. Take the inter-terminal AirTrain to Terminal 1. From the moment you step off your CLT-JFK flight until you arrive at the security area at T1 should take maybe 20 minutes, leaving plenty of time to clear security and get to your gate.

If, however, you want to try to arrive earlier, you have two options:

There is a 405p RIC-CLT-JFK connection that would get you into JFK at 1017p. Without checked luggage, you should be able to standby for this.

There's also a 604p RIC-LGA nonstop that arrives LGA at 730p. A sympathetic gate agent might let you stand by for this flight, which would give you six hours to get from LGA to JFK (albeit at your own expense: $7.75 by public transportation or about $35 by taxi or uber).

I don't know what the fees are for non-status passengers to travel standby, but I recommend only dealing with the gate agents (who have the most authority to bend and break rules) and not with the ticket agents (who have much less authority). Check in for your regularly scheduled flights in order to get through security at RIC. If you arrive at RIC early enough, go to the gate for the 405p RIC-CLT departure and ask about standing by. If you clear this flight, they will not be able to confirm you on the CLT-JFK connection -- you'll need to stand by for that as well -- but worst case scenario is that you'll end up on your originally scheduled CLT-JFK connection, and best case scenario is that you'll make the earlier one.

If you can't get to RIC early enough for this option, try to get there early enough for the RIC-LGA flight. Again, speak to the gate agent, not the ticket agent. Explain that you have a very tight connection at JFK to an international flight, and that you'd prefer to take the LGA non-stop, even though that means having to get from LGA to JFK at your own expense. This probably is not permitted by the rules of your ticket, but a sympathetic gate agent working a flight that has seats that are going to go empty in any event might be willing to help you out.