Currently there are no dedicated permission settings in Structure.Gantt. The chart has the same permissions settings as the structure it is based on. Users with the View permissions can only view the Gantt chart. Users with the Edit permissions can work with the task bars in the chart and make changes. Users with the Structure Control permissions can change the Gantt Chart settings.
All standard Jira permissions are applied too – you need the Edit Issues permission to change the fields, create links, and so on.
Gantt Chart configurations have their own permissions logic. By default the configurations you create are not shared with anyone else, so they are not visible in the available configurations list for other users. If you use such a configuration to build a chart for some structure, other users will be able to work with the chart (based on the structure permissions), but will not be able to see this configuration.
You can share the configuration with all other users by selecting the corresponding option in the configuration general settings. Once shared, this configuration will be visible in the read-only mode in the list of configurations for all users.
If you create a configuration without specifying the owner, any user will be able to change it.
If you want to delete a configuration, which is used in an least one chart, you will need to select a configuration, which will be used instead of it. For shared configurations you will need to select another shared configuration. If, however, you do not have permissions to modify those charts, you will not be able to do it.
Jira admins can see and edit all configurations.