As @Trudy Claspill indicates, there's no a native way of using issue count in the Burndown gadget. We provide a commercial app called Dashboard Hub for Jira, which provides more than 60 different gadgets and metrics, custom charts, etc. Our Burndown chart gadget allows you to select different estimation statistics, like issue count (also story points, time estimate...).
Hope this helps!
You cannot do that with the native Burndown gadget. A request was opened for that previously, but Atlassian has marked it as Won't Fix.
I found another community post that mentioned a third party app that might help. There are probably other third party apps that could also help.
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