The Jira Align Team is currently working with Atlassian U to develop a series of both Online and Instructor Lead/Publicly available classes. Unfortunately, we do not yet have a date for general availability, but I'm sure there will be a boisterous market announcement, as these are ready.
Is your company currently implementing Jira Align? If so, you would work through your Jira Align leader to get into the proper training.
To my knowledge, there currently are not any public classes, as Jira Align is custom configured for each client in multiple dimensions.
Jira Align training is currently delivered as part of the implementation process in an in-person classroom training environment.
Depending upon your role in your company, you might be able to get access to Launchpad, a guided learning demo-type environment. You would need to reach out to Jira Align Sales to get access to Launchpad.
Atlassian University has completed the design of the Jira Align Program Essentials course. The link below describes the scope and focus of the course.
The url still includes "agilecrafthelp" because Jira Align was known as AgileCraft until the acquisition last year.