What is the coat fabric? If this has any wool in, one way of getting this flat is to use a wet cloth and hot iron to press this and then use a clapper - i.e. a wooden gadget and hold this down over the area. If you do not have a clapper, then a wooden (clean though) rolling pin will work wonders. Wooden rolling pins are relatively cheap, and if you have to get one then please keep this in the sewing room and use only for this purpose. For some reason the wood absorbs the steam created and gives a lovely finish. If in doubt about this use some scraps of the coat fabric, make a little seam, press and use the clapper or rolling pin and see the difference. Banging away with the wooden gadget whatever is is very satisfying and can make such a difference to anything that is rather bouncy.