Hey Jacques, I see that this is a rather old question, but I happened to stumble upon it and thought that I might answer it in the case that you might still be interested in a solution to your problem.
You can use the Version Report, which displays a team's progress towards completion of a version. The Version Report also shows the predicted release date based on the team's average rate of progress since the start of the version, and the estimated amount of work remaining. All you would need to do to use this report is append a single fix version to each of the issues in your project. You could do this through a simple bulk change. You could then continue to use sprint burndown reports to view and report on individual sprint burndown.
Also, the Epic Burndown report could be useful in this situation, if your overall project happens to operate using a single epic.
Both the Version Report and the Epic Burndown report can be found on the left-hand side of your JIRA board, under "Reports." There is also a useful Version Report gadget in Confluence, which will display the same thing if you configure it to do so.
Hope this helps,
Schuyler
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