Apple - Disable F14/F15 for Brightness Control

The Display section in Keyboard Shortcuts shows up when a third-party (non-Apple) keyboard is attached (I used a USB one, I don't have a wireless one to test). From there I was able to disable the shortcut keys.

Once I was able to disable them, I did some digging to find where the preferences are stored behind the scenes. Turns out that they live in ~Library/Preferences/com.apple.symbolichotkeys.plist.

Setting the enabled property to false for keys 53 through 56 of the AppleSymbolicHotKeys dictionary, will disable the F14/F15 brightness adjustments (this doesn't affect the F1/F2 keys on Apple keyboards).

/usr/libexec/PlistBuddy -c "Set :AppleSymbolicHotKeys:53:enabled false" ~/Library/Preferences/com.apple.symbolichotkeys.plist
/usr/libexec/PlistBuddy -c "Set :AppleSymbolicHotKeys:54:enabled false" ~/Library/Preferences/com.apple.symbolichotkeys.plist
/usr/libexec/PlistBuddy -c "Set :AppleSymbolicHotKeys:55:enabled false" ~/Library/Preferences/com.apple.symbolichotkeys.plist
/usr/libexec/PlistBuddy -c "Set :AppleSymbolicHotKeys:56:enabled false" ~/Library/Preferences/com.apple.symbolichotkeys.plist

The change will take place after a logout or restart. If you want to re-enable them, change false to true.

robmathers answer is correct in spirit, but didn't work for me on Retina iMac 27" (2017) with full-size Apple Magic Keyboard 2 on macOS Sierra 10.12.6. The plist keys in the com.apple.symbolichotkeys.plist were different. Here are the commands that worked for me:

/usr/libexec/PlistBuddy -c "Set :AppleSymbolicHotKeys:7:enabled false" ~/Library/Preferences/com.apple.symbolichotkeys.plist
/usr/libexec/PlistBuddy -c "Set :AppleSymbolicHotKeys:12:enabled false" ~/Library/Preferences/com.apple.symbolichotkeys.plist

Don't forget to restart the computer (simply logging out doesn't work). After this is done you'll be free to map these keys.