@jahbread,
You can replicate the problem by using curl.
curl -O test.mp3 https://www.jahbread.com/wp-content/uploads/2016/11/Blacks-With-Power-Pilot.mp3
Results:
HTTP request sent, awaiting response… 302 Moved Temporarily
Location: /wp-content/uploads/2016/11/Blacks-With-Power-Pilot.mp3 [following]
https://www.jahbread.com/wp-content/uploads/2016/11/Blacks-With-Power-Pilot.mp3: Redirection cycle detected.
To see the cookies:
curl -I https://www.jahbread.com/wp-content/uploads/2016/11/Blacks-With-Power-Pilot.mp3
I cannot speak for Google play or Stitcher, it may be that they setup their HTTP media download library to accept cookies. I can tell you that most podcast apps and specifically iTunes iOS and Desktop apps do not use cookies.
In the headers the cookie is using a variable named mplk, if that helps. that may be the abbreviation for something on your server. I should also note that I do not see PHP in the headers, so this may be an issue on the server rather (e.g. .htaccess file issue) than an issue with PHP or a WordPress plugin. There are also headers for WishPond, so that may also be doing something with your .htaccess file you’re unaware of.