Every now and then, the question pops up, why does atlassian invites to use subtasks, but they dont show in the Burndown chart.
The answer is: no, that does not work. Some people help themselves with add ons and twisting and configuring them, that it somehow works out.
But until now, Atlassian did not provide a simple solution to that simple demand.
However, my personal solution is, that I reorganize my projects and boards in a way, that a story/task is the lowest level in my boards. As they are shown in all charts when closed, they need to be refined as much as possible, to have a chance to be set to done in one single sprint.
Enjoy!