Will my bankruptcy from gambling debt affect my son from getting a job that requires secret security clearance?

No checks are done on family members other than a spouse and that is only for Top Secret. As long as his name is not on any of the accounts that are affected then there would be no reason for concern.

In that case why they are asking for parent and siblings name in SF-86 form for secret clearance. What are they checking?

Foreign citizenship of immediate family members is a concern for security clearances.