When configuring a Jira integration, you can map the Epic % complete field in Aha! to the Epic % complete (issues completed) field in Jira.
According to https://www.aha.io/support/roadmaps/strategic-roadmaps/roadmaps/visualize-progress-on-roadmaps#map-progress-in-integrations, Jira calculates the Epic % done field by calculating the percentage of child issues in Jira that are in the epic's Jira project and have the status Complete. It is not a field that will directly show up in Jira.
In order for that field to work properly, Aha! Roadmaps needs to know about child issue types that contain a Parent field which links to the Feature epic custom type.
It would be helpful to see an error message in the Aha! integration mappings if this Epic % complete field is integrated and Features (or whatever the child records are) are not integrated. Without it, this integrated field won't work and nothing tells you why.