How about developing a Jira plugin from the app?
Then you would have combined the planning poker directly with the JIRA issue tracker.

Links to the plugin development documentation:
Jira Cloud: https://developer.atlassian.com/cloud/jira/platform/getting-started-with-forge/
Jira Server: https://developer.atlassian.com/server/framework/atlassian-sdk/set-up-the-atlassian-plugin-sdk-and-build-a-project/