Compared to more modern tools Jira is actually not very flexible.
For me the most flexible and useful tools are Kanbanize[0] and Kaiten[1].
Both companies are engaged in furthering the Kanban method which also means they care about having a lot of features for displaying cards, limiting work in progress, defining workflows and have solutions for working together on bigger workflows with several teams.
I use both professionally.
A lot of other solutions have assumptions built in which really limit flexibility. One example in Jira is the coupling between workflow status and columns on boards.