I hate to be the naysayer here but the cloth side goes to the window, sandwiching the rubber side between it and the drape otherwise the sun beating directly on the rubber will rot it in no time. Just treat it like any insulated lining.
I'm making drapes for a bedroom and here in FL the sun is brutal too....I have two windows, one facing east and one facing south....the black out lining I got had the cloth on the outside as did all the other insulated linings.