No shortcuts for Gimp 2.8, also no symmetry tool and no clipboard mask 
You can open a brush as an image - right click on the brush icon.
That is flipped with the flip tool.
Then two options
IF a coloured brush, copy to the clipboard and use the clipboard brush
or
IF a greyscale brush that takes the FG colour, no easy way, export that as a separate flipped greysale brush.
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edit: Pulled an old script out of my archive. Attached un-zip Put in your C:\Users\"yourname"\.gimp-2.8\scripts folder
Originally for Gimp 2.6 which did not have those brush controls. There is an option to mirror the brush.
30 second demo: https://i.imgur.com/mT9a6ne.mp4
You can open a brush as an image - right click on the brush icon.
That is flipped with the flip tool.
Then two options
IF a coloured brush, copy to the clipboard and use the clipboard brush
or
IF a greyscale brush that takes the FG colour, no easy way, export that as a separate flipped greysale brush.
-----
edit: Pulled an old script out of my archive. Attached un-zip Put in your C:\Users\"yourname"\.gimp-2.8\scripts folder
Originally for Gimp 2.6 which did not have those brush controls. There is an option to mirror the brush.
30 second demo: https://i.imgur.com/mT9a6ne.mp4