Wow ! I really wish I could come with you on this one.
There are direct trains but no direct flights for this journey. kolkata (West Bengal) to Jammu (Jammu And Kashmir) distance is 1742 km and you can get there by flight + flight in just over 6 hours and 40 minutes or by train fares starting from ₹ 612.
Whew - Man! It's hot as hell there!