The flickering is probably caused the the shape of your wick. Take a sharp pair of scissors and trim the wick so that it is curved, an arc or a dome shape, not just flat across the top.
I have the same Weems & Plath lantern. I like the heavy construction, but I find that having to take it apart to light the wick is a real hassle. My Pearson also came with a small, gimballed lantern that is probably a W&P, but the globe is missing. I need to run down to Annapolis and see if they sell replacement globes because I'd really like to use it.
I'm a big fan of oil lamps vs. burning up the battery for light at night. Don't get started on me about LED's. I know they're out there.