Thanks for asking. As detailed in https://about.gitlab.com/direction/#scope we plan to add Huboard as a kanban board and there is currently a bounty for that https://github.com/huboard/huboard/issues/276

A burndown chart is something we planned to do now that we have issue weights. I couldn't find the issue for it so I created on https://gitlab.com/gitlab-org/gitlab-ce/issues/13422