Risu, well if your going to use your own pattern I would go for cotton, either bought by the metre, or use egyptian cotton sheets! easily found easy to dye! two to three layers of cotton sandwhiched together would give the necessary thickness, and allow the coat to hang right and crumple with wear. You could also line the coat halfway from the top to the waist with a slightly heavier fabric? this would give the coat thickness but still allow it to move and crumple like Deckards! I have a cotton lightweight dressing gown that hangs and creases up like the screen coat, in fact it would be an easy and cheap task to modify this into a Deckard trenchcoat, cheap too!
Off course this all depends on what use you have in mind for the coat? an occasional wearing at conventions or more day to day wear?
The Blade Runner costume department didn't have such a problem, they used various coats on set, depending on the specific scene, lightweight version for stunt work, more detailed for closeup!
Kane2122