Hello, 

Assuming a few things

• The parent job triggers the child job programmatically
• By "job id" I am assuming you mean the job run ID (the actual execution instance), not the static job definition ID.

Trigger the child job using jobs/runnow. The response will give you the child's run_id.

Optionally wait for the child job to finish, if the parent depends on it, using jobs/runs/get