BY FLIGHT : There are 2 flights come to Srinagar by Kerala like Jet Airways ,Air India but they are multiple flights they all operates daily and take 23 to 25 hours to reach Srinagar with one or two night stay in Delhi.
BY TRAIN : There is no direct train from Kerala to Jammu so first you take Kerala express to reach Delhi & than to take another train from delhi to Jammu. The major trains are Jammu Rajdhani express , Uttarsampark Kranti , Jhelum Express , Duranto express , Shiv Shakti Express , Shalimar express, Jammu Mail , Andaman express , All Jat express , Malwa express , Durg Jat expressthe total distance is 3250 kms but train drops you at Jammu Tawi Railway and than you choose taxi for further journey.
BY ROAD : There is no bus service or operator from Kerala to Jammu Kashmir. You take bus from Kerala to Delhi ISBT i.e. 2700 kms 40 hours to reach delhi & than take another Bus from ISBT Kashmiri Gate Delhi to Jammu Bus stand the approx distance is 600 kms & it will take 11 hours approx to reach Jammu by road. In Jammu there are various option to reach Kashmir you take local sharing Cabs local bus service and individual cabs . Bus service operates in the night only you take Volvo buses as well as local buses from Jammu Bus stand & rest services like individual taxi & sharing cabs you take from exit point of Railway station , Jammu Bus stand & Gumat chowk they operates whole day. The distance between Jammu to Kashmir is approx 300 Kms & it will take 8 to 10 hours to reach Kashmir.