There's nothing in the wiki that says there are any particular dishes you can't cook on the cookout kit. I haven't used it a lot, but I've been able to cook anything on it I wanted to. It should act similar to the kitchen. When the kit is activated, it gives off a smoke animation. You have to have all the ingredients in your inventory, and be close enough to the kit that you can open it up. Any recipe you know that you have the ingredients for should light up in colour, and you click on the icon to create the item. Just like crafting. In the attachment screenshot, you have the rice but not the fish (anything labelled as a fish will work) or the seaweed.