Is there a genetic aspect to esophegian cancer and what approach should one take to monitoring?

No. The huge majority of esophageal cancers, both squamous cell carcinoma and adenocarcinoma, show no tendency to run in families. Unless your physician disagrees, having a family member with this cruel illness is not a reason for you to get endoscoped, or do anything more than anyone else (avoid tobacco, excess alcohol, stay trim, manage reflux).
No. Esophageal cancer is unlikely to be genetic in origin. It is most likely due to exposure to major toxins such as tobacco and alcohol.