Remote URLs
BIRT reports have a concrete URL on JIRA and they can be shared among users (by email, as links on the Internet, etc):
${JIRA BASE URL}/plugins/servlet/birt/run?__report=${report.rptdesiign}
Encode Report Names
Of course, you have to replace the variables above ${} by their values according to your JIRA instance. The ${report.rptdesign} variable must be encoded to avoid issues with special characters like blank spaces, etc. You may want to use online services like this to encode BIRT report names easily.
Configure the final report
The BIRT Viewer supports some parameters in the URL to configure some report details like hiding some buttons and other options. Those parameters are described in this page.
Security
Sure you are concerned about security. What it happens when a BIRT report link is shared?, who can view it?, what do users see? Well, all the BIRT reports displayed anywhere (JIRA Dashboards, Confluence pages, etc.) are BIRT reports URLs embedded in iframes. As BIRT reports rely on the SQL for JIRA Driver to fetch data in a secure and private way, a JIRA user's session is always required. In other words, you have to be logged in JIRA prior to see any data on a BIRT report and, of course, all those data are fetched under the logged in JIRA user's security context: it means different users may see different data if they have different permissions on JIRA. But you do not have to worry whether someone access to the BIRT report accidentally or by error: