Task Timing Manegments

Is there any chance to we have timing conflict by assignment task for special users.

Project Leader A from project A1 assign task T1 add 01-01-2019 to 02-01-2019 to special user U1.
Project Leader B from project B1 assign task T2 add another by same 01-01-2019 to 02-01-2019 to special user U1.

How project managers discover free time of U1 during assign task and time conflict?
How U1 knows about timing conflicts between projects tasks?

I think everything you are asking is possible to add with a plugin but have no knowledge of a plugin with such features.
You can try the gantt plugin, it will show you a Gantt chart based on tasks start and estimated end dates. Then you can filter the tasks by an specific user and see if any tasks are overlapping each other.

non of similar apps dosnt such as feature, i think it’s require for manage human resource layer for assignment of task.

May be my mine set is wrong about this but as developer i think it’s very essential for project and human management.
Why should be plugin?

I think design also must be User design follow instead of just project design follow.
for example in rest apis always we see the main request params is project_id as cetner of many requests.

I didn’t say it should be a plugin, I said it might be possible to implement on a plugin, if you want to, because what you’re asking for is not available on kanboard yet. You can either change kanboard’s code or develop a new plugin.