I hope you get good sleep along the way coz this might take long
There are direct trains but no direct flights for this journey. kolkata (West Bengal) to Rishikesh (Uttarakhand) distance is 1305 km and you can get there by flight + cab in just over 9 hours and 33 minutes or by train fares starting from ₹ 510.
The weather at Rishikesh is varying from "nice" to "hotter than nice".