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My team is not interested in following the principle of Jira tickets only flow forward on the board and rework happens in whatever column the problem was found.
I don’t share this method with the team but I don’t want to cause resentment but I believe it distorts the board and hides bottlenecks and disfunction.
Should I be democratic and allow them to move tickets back and forth and persist with making them understand why tickets should move forward only?
Is it working? Then don't stress it.
There are some schools of Kanban that adhere to what you are saying. It is not, however, a hard and fast rule. I tend to teach and use a two-way Kanban board as I've found it more effective.
The key to a two-way board is WIP limit. If you move something from test, back to development, then you may have to remove something from development back to the backlog queue.
Check out the slide 11, Using WIP limits, in my Requirements to Done Flow presentation for a visual example of this. It's animated so go into presentation mode.
