Ask your local PO for one of their thickness guides, so you can check for yourself at home whether an item will fit through the slot.

If packing clothing, I always use a sheet of lightweight cardboard (e.g. one side of a cereal packet) and fold the clothing around it and then place in a plastic bag which can be sealed tight after expelling the air. The cardboard prevents the item squishing up to one end, and jamming in the sorting machine.

It's also a good idea to get yourself a set of scales so you can check just how much your item weighs, and therefore have a far more accurate idea of postage cost.