Search XML file from within WordPress?

Here’s a PHP library which uses SOAP calls to access JIRA: https://github.com/jrbeeman/php-jira

However, if you can get the XML file into a place PHP can access it then you can use general PHP calls to parse and read the XML file, e.g. SimpleXML http://php.net/manual/en/book.simplexml.php

From there you can put your code in a theme template or a plugin. Nothing WordPress specific needs to be done to gain access to the JIRA export, your wordpress code would merely be UI over the top.