The new Atlassian App Migration Platform (currently under development) will enable all Atlassian Marketplace Partners apps to build automated migration paths for their apps.
When a customer migrates projects from Jira Server / Data Center to Jira Cloud using the Jira Cloud Migration Assistant, the app migration platform will coordinate with Agile Cards to automatically move AC templates and cork board's configurations to be used in your Cloud instance.
Spartez Software is currently working on the possibility of migrating Agile Cards data, i.e. templates and cork board's configuration. We plan to provide this option for our clients by the end of January 2021.
There is currently no process, manual or automatic, to migrate your Agile Cards data from Server/DC to Cloud.