Hmm, I haven't done an import like this specifically. Let's go over your options:
Are you a Trello Business Class customer? If so, you have access to CSV export functionality. You also can export all boards to JSON. For JIRA Cloud, imports are a little more locked down than a JIRA self-hosted version. You can see the list of Atlassian Cloud Restricted Functions here.
Anyway, if you have access to CSV exports, you can look into this option: Importing issues into JIRA Cloud using CSV files, FogBugz OnDemand, Pivotal Tracker and Trac (This option seems pretty straight forward)
If you only have access to JSON single board export (not a trello buisness class customer) or you'd prefer to do a JSON import over the CSV option AS a business class customer, you should look in to this option: Importing Data from JSON (this process goes something like, stand up a self hosted version of JIRA on a trial license, import via JSON into that project, WEBDAV connect to JIRA cloud and import the data from your self-hosted JIRA)
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