Checklist for Jira is available for iOS, Android and native Mac applications.
To use the add-on in mobile or native apps it should be displayed in glances.
Make sure you are using the new Jira issue view.
In the add-on preferences turn the "Display checklists in Issue Details section" preference to OFF:
This will switch the add-on to be displayed in issue glances, and you will be able to use it in native/mobile apps:
Tap the “Checklists” glance to open the checklists panel