Try replicating the below in a terminal:
Determine that your user is the user that you expect it to be when you run the rest of the commands below:
tmartin:dart:~> whoami
tmartin
Try to manually change to the directory that Sublime is having problems writing into:
tmartin:dart:~> cd ~/.config/sublime-text-3/Local/
Try to create a sample file in the location to verify that this user can create files here:
tmartin:dart:~/.config/sublime-text-3/Local> touch sample.txt
Remove the sample file created above (just to keep things clean):
tmartin:dart:~/.config/sublime-text-3/Local> rm sample.txt
If any of these steps fail, that will help point in the direction of what’s going wrong for you.