If you're looking for per-icon permissions, check out the PERMISSION attribute.

Permissions for players:

Permission Description<file>.yml

Required to open a specific menu (through the configurable command, from other menus, with signs, or with admin commands).

Replace <file> with the file name of the menu you're giving access to.
The file name must not contain spaces!

Permissions for administrative commands:

Permission Command /cc help /cc open <file> /cc open <file> [player]
Note: this permission also grants access to open all menus.
chestcommands.command.list /cc list
chestcommands.command.reload /cc reload

Permissions for administrative features:

Permission Description
chestcommands.sign Required to create menu signs.
chestcommands.economy.bypass Bypass economy costs.
chestcommands.update Receive update notifications on join.