Our app User Profiles for Jira Data Center and the one for Jira Cloud have differing conceptual ideas for addressing some of the use cases. Furthermore there are technical constraints in Cloud that impede automatic migration. Therefore, we do not provide an automated migration path.
Instead, we can in all conscience recommend starting from scratch in Jira Cloud, as this can be configured very easily and quickly.
In more detail, the profile elements that a custom field shows can be grouped into two kinds, and each group can be handled differently for migration purposes:
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Profile elements synced automatically with data coming from LDAP, configured via “Mapping for LDAP Attribute(s)”
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Profile elements filled manually in Jira, by each user for themselves
Fields synced with user data coming from LDAP / Entra ID
The 1st kind of custom fields (using Profile elements synced automatically with data coming from LDAP) can be migrated to Cloud by manually creating an appropriate custom field in Cloud, see docu Custom field configuration | Create custom field.
Example 📝
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Old (Data Center):
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Field “Assignee’s Manager”
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for reference user field: Assignee
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using a profile element: “Manager”
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mapped to LDAP attribute via:
%%manager%%
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→ New (Cloud):
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Create field “Assignee’s Manager”
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for reference user field: Assignee
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using Microsoft user attribute: “Manager”
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Fields filled manually in Jira Data Center
For the 2nd kind of custom fields (using Profile elements filled manually in Jira), first it must be decided if their values can be moved to attributes in Microsoft Entra ID:
Yes, data can be moved to Entra ID 
Those custom fields can be migrated, like so:
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Move data to Entra ID (out-of-scope of our app; must be done by customer)
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Create custom field normally, as described on Custom field configuration | Create custom field
No, data cannot be moved to Entra ID 
Those custom fields cannot be migrated to User Profiles for Jira Cloud.