Hello! Is there a way in netsuite to configure a user to receive email notifications on REST web services failures (ie; FloQast for example)?

No native setup for REST WS failure emails (unlike SOAP's saved search on Execution Log for errors), but monitor via Execution Log (Setup > Integration > Execution Log); filter for REST failures (status = Failed, type = REST). Subscribe a saved search to email on new fails, or use SuiteScript to scan logs and notify. For FloQast, check their side too.