Yes, a 14-year-old can get varicose veins, although it's less common than in older adults.
While varicose veins are more frequently associated with older individuals, they can develop at any age if circulation isn't flowing properly. According to the reference article "Even Teenagers Can Develop Varicose Veins", while senior citizens "still have the market cornered on vein issues it is possible to develop them at any time during life if your circulation isn't flowing properly" (Even Teenagers Can Develop Varicose Veins. 16-Nov-2020). This means that teenagers, including 14-year-olds, are not immune.