How can we measure the progress of a task in Kanban? Also will there be an estimate for a task or is it simply saying that focus on the task and finish it rather than sticking to the deadline ?
In my opinion, I would always include an estimate against any Kanban task, as this helps you limit the number of tasks that are undertaken at any one time (Work in Progress Limit). You can also calculate your team's velocity, which can be immensely helpful in future planning scenarios.
Regarding task tracking, there are a number of different ways that you could do this. The most common way would be for your team to add time/percentage against the task until it has been completed.
If you wanted a more top-level overview of tasks, you could consider adding additional columns to your Kanban board. An example of this in the Web Development industry could be:
Blocked | Backlog | In Development | Testing | Pull Request | Complete
This provides you with a more visual way of tracking tasks, which is key to a successful Kanban approach.
If we're talking about Kanban in its strictest sense - the measure is the lead and cycle time of tasks as they get through the flow. Look up CFD, or Cumulative Flow Diagram, for more info on this. There is no need for estimates - you just pick up the next task in the queue - so it really doesn't matter whether the task is Large, Medium or Small - you work on the next most important task - and if that takes many many days (equivalent to a "Large"), then that will impact the cycle time.