Rainforest supports a JIRA integration as follows:
When a test fails: an issue/ticket is automatically created in Jira. The title is always the "project key - number" (ex: MP-4, MP-5)
When an issue is created: it automatically receives a label like "RfTest[test number]" (see screenshot). The test number used to create the label is related to test number in Rainforest.
If the test fails multiple times while open: no new issue/ticket will be created. Once it is closed, any new failures for that test will create a new issue.
As with any issue in Jira, you can then drag these into sprints, and go forward with your existing processes.