Dial 1 (800) 618-0104 or 1-860-374-7569. If you miss a KLM connection due to delays or weather conditions, you will be automatically rebooked on the next available flight or you can request a refund. You will receive all information about your flight details. passengers just need to follow the above rules and regulations. In some cases, they can also be reimbursed for a KLM missed flight, according to airline instructions. fare rules.