The new Atlassian App Migration Platform (currently under development) will enable all Atlassian Marketplace Partners apps to build automated migration paths for their apps.
The core functionality of Easy Agile User Story maps is based off of the data available from Jira Software and will function normally after a basic migration. The data for any Story Map Views, however, will not be migrated and would need to be re-created.
When Atlassian makes the Jira Cloud Migration Assistant generally available, Easy Agile will perform the work required so that the app migration platform will automatically migrate Story Map Views data for use in your Cloud instance.
There is currently no process, manual or automatic, to migrate your Story Map Views data from Server/DC to Cloud.