Select the Polygonal Lasso Tool in the Constrained Mode, as (for me, at least) it is much easier to use than Freeform Mode, but in the end it'll still be your choice.

Make sure you are in the Flats layer all the time during this process.

Start tracing the outside of your lineart. Try to keep it very tight inside your lineart.

After you've closed the selection, you will have something like the image at the right.

Select a mid-Gray color on the Swatches palette, like this, and fill your selection with it.

What I basically did here is to separate the foreground (Gray), and the background (white), although with my preference the background is already located on a different layer.

TIP: While at this stage of creating your flats, go to the layer's Lock Options and click on 'Lock Transparent Pixels' to avoid coloring outside the outlines.