I'm very much on the bottom rung of the ladder and have flagged around 1 kid a year on average. All I see of it is getting one of the safeguarding team asking exactly what happened, putting it all in writing and it's then out of my hands.
There does seem to be a hierarchy of training that goes teacher > safeguarding bod > DSL > police/social services but I don't know the details behind the qualifications needed.
From my end of the spectrum it tended to be slightly more direct, being responsible for nursing patients who were either known to be at risk, or there was a suspicion of abuse.
Safeguarding is very admin heavy, comparative to what one normally would do for a patient.
Documenting injuries (from a neutral perspective), incident reporting online using the Datix system, which is really long-winded but comprehensive and cc's everybody who might need to know, then both emailing and phoning the appropriate social services, and if that wasn't enough completing the local forms to be added to the patient documentation (that I would judge to be the arse covering bit).
I don't know what the expectation is for teachers, but as
@mush_dad has pointed out, pretty much all patient facing staff annually do level 1 safeguarding training and in the trust I work for all clinicians who are band 4 and above have to complete level 2.
I assume that's pretty much across the board within the NHS.