I have found them here for the Beta 1.02: C:\Users\USERNAME\AppData\Local\Frontier Developments\Elite Dangerous\Options\Bindings\
There are 2 files of interest: "Custom.binds" and "StartPreset.start"
gaming.stackexchange.com/users/83620/intrepidis
If you copy the Custom.binds file to MyName.binds (or something) it will appear in the drop-down menu for you to choose from.
gaming.stackexchange.com/users/91737/Grim...
I think I found them!
I don't know if they added them since the beta came out, or what.
But It looks like custom bindings are saved in a file here:
\Users\USER\Local\Frontier Developments\Elite Dangerous\Options\Bindings
gaming.stackexchange.com/users/76799/Deathnozzle
On the Mac they are stored in : ~/Library/Application Support/Frontier Developments/Elite Dangerous/Options/Bindings Where ~/ is your user folder /Users/<your_user_name>/Library/Application Supp...
gaming.stackexchange.com/users/126342/dwkns
Found it a bit silly i couldnt just add comments for clarification but can provide a new answer.
Regardless, just to update / concur:
Elite Dangerous Horizons V2018.12.17.190809 Location: C:\Users\ USERNAME \AppData\Local\Frontier
Developments\Elite
Dangerous\Options\Bindings\
AS stated previously;"There are 2 files of interest: " Custom.binds " and " StartPreset.start ""
But you dont need to do anything with the startpreset file,
when in-game that file will update to whatever you last 'loaded'.
When COPYING to make additional config profiles, as stated in a comment by GERT.
You need to edit the PRESETNAME inside the file as well as the actual file name.
What i noticed was that the baseline Custom.binds file didnt have that option
but i had an extra file called custom.3.0.binds which did have a preset.
So copy that one, edit the file name and preset inside the file, save and reload your game.
I did all this in testing setup for a 3D mouse (3Dconnexion) for very fine controls esp for docking [which i was only able to get working by using ControlMyJoystick as by default this does not work well at all].
gaming.stackexchange.com/users/224619/B1llaB0ng23
I'd like to easily backup my controls in Elite: Dangerous. Does anyone know where the controls are stored, or a way to find out? Thanks!
Where is the file Elite Dangerous stores the controls?
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<elite-dangerous>
gaming.stackexchange.com/questions/168401
gaming.stackexchange.com/users/76799/Deathnozzle
 If you copy the  Custom.binds  file to  MyName.binds  (or something) it will appear in the drop-down menu for you to choose from. Elite Dangerous seem that stores key bindings in files that are located in specific folders..
The community states the location of the files.