The Server/Data Center version of Epic Time stores information and displays it via the custom fields.
The Cloud version of the app doesn't store information and retrieve it via on-the-fly calculations when a user opens an issue / gets the report using Original Estimate field values and work logs. That is why you do not need to migrate the values of the Epic Time custom fields while migrating on Cloud:
- Migrate the values of the Original Estimate system field;
- Migrate the work logs;
- Add the Epic Time app to your Jira and get the Epic Time values in the relevant sections.
Note that unlike the on-premise version the Cloud version will not allow you to use the Epic Time information anywhere else: as a column in Issue Navigator, in standard Jira reports, etc.