Driving from Chennai to Jammu is not advised since it takes 46 hours approx. There are plenty of flights via Delhi which take a minimum of 8 hours to reach Jammu. There are also trains routes to Jamm (Read More)u from Delhi which can be very comfortable depending on how you go about it.
Since the distance between Kolkata and Jammu is around 2000km, it is not advisable to travel there by car or bus which takes around 30 hours approx. You can travel to Jammu by flight which takes arou (Read More)nd 6 hours. The journey by train is 36 hours long but is quite comfortable.
So if it suits your budget the best way to travel from Kolkata to Jammu is by flight.