"will they automatically flag my sons SS number and not process my return or will they refund it and just wait for his paper work and my amendment to go through "
Amendment processing is quite separate from original return processing. Hence, I imagine that if your return had only the Child Tax Credit, that it would come back in the usual 21 days that the IRS quotes. But if your return is asking for the Earned Income Tax Credit or the Additional Child Tax Credit, refunds won't even begin processing until March 3, 2025. See What to Expect...
However, really, amendments are processed in months while original returns are processed in weeks. They won't flag anyone's original return because an amended return uses the same SSN for a dependent - indeed, they won't even notice.
It may take months for all of this to even out.