You should first seal / create a vapor barrier on the surface of a concrete slab and side walls of that space under the floor frame you’ve created. You can use thick plastic foil for that purpose (e.g. 6-mil layer).
Unless there’s a rigid insulation on the exterior of your side walls, you should install it on the interior (see the image below), go over it with plastic applied to the concrete floor, and taping its entire edge to create an air tight envelope. I believe your last sentence applies to the side walls but I’m not sure… if so, it might be difficult to secure duct tape and create an air tight seal.
After that you can fill the space with insulation, no second vapor barrier is necessary or critical at this point (directly under the floor decking).