Welcome to the WMF, Allen!

It´s a "Feldbluse", 2nd type. Later variations have a fleece patch on the upper right sleeve to attach velcro patches. The patch you have is the obsolete one from former Heeresfuehrungskommando (Army Forces Command, active 1994-2012). Your patch was worn on the upper left sleeve of the Dienstanzug (firts class uniform). The command had a different subdued patch for their combat dress which I can post later.

I don’t think that is a smock. It looks like a padded reversible winter coat. Oak reversible to white.

Got this from a thrift store in my city. I know absolutely nothing about German military gear but I know that only 5 USD is pretty cheap for this jacket. I have a patch that I think goes on this jacket. Does anyone have any insight on where I would put it (if it even goes on it)?

https://ww2wings.com/wings/btw/bulgaria/bulgaria.shtml

The OP wings are regulation from 1951-1959

ABOVE: This is the branch of service insignia for Austrian air force personnel. Gold for officers. Not a pilot qualification or rating badge.   BELOW: This is from the current Austrian Defense forces website (https://www.bundesheer.at/unser-heer/uniformen-und-abzeichen/abzeichen). Current pilot badge illustration. Seems to be in line with the same design that has been worn throughout post-war republic through the cold war until now. Difference would be in materials and construction.   

"The enthusiasm which aviation had aroused in all social grades brought together a number of persons who founded, on April 2, 1913, the Aero Club of Chile, which was incorporated July 4 of the same year. The first officers were: President, Don Enrique Phillips; vice president, Alejandro Weber; secretary, Don Armand Venegas; second secretary, Don Armando Fernendez; treasurer, Don Juan A. Maluenda V.; directors, Senors Ernesto Aguita, Manuel Barros B., Paul Furet, Juaquin Jelvez, Osvaldo Jimenez, Julio Kaulen O.; Eduardo Molina Lavin, Bernardo Morales, Augusto Perrey, and Erasmo Vasquez." Pan American Union. 1919. Aviation in Chili and the crossing of the Andes. Bulletin of the Pan American Union, Volume 49, page 300   Published in the Aeronautical directory of 1920:  

Thank you for looking it over.

I have not seen a club wing before from Chile, just their military wings. But based on the construction and the large screws and bakelite backing I would date these to the 1940s.

The Blue is Ribbed Twill Gabardine, Wool, the Sleeve Lining, Poplin, Cotton we should think.

Michael Caine took over the lead role in the play from Peter O'Toole when O'Toole left to star in Lawrence of Arabia. Once again the inaccurate wardrobe, this time with the Jungle Green Battle Dress, this came out what in 1943 right.