From those two shots you see some unique details that should help narrow down the search:
Raglan sleeves and NO epaulets.
Double-breasted front closure
Buckled straps on the wrists
Right front shoulder storm flap (sometimes called a "gun flap")
Rear shoulder yoke looks like it may be loose, but hard to tell
The main thing is to find a trench coat with raglan sleeves and no epaulets... but in a style that usually has them (the traditional "Bogart" style trench).
![TOH :TOH:](./images/smilies/Indy-Hat-Tip.gif)