Whoa - that looks like an exciting journey to take !
There are direct trains but no direct flights for this journey. kolkata (West Bengal) to Jammu (Jammu And Kashmir) distance is 2044 km and you can get there by flight + flight in just over 6 hours and 40 minutes or by train fares starting from ₹ 612.
It's gonna be warm and sunny, and did I mention warm ?