But how are they training those scribes without anyone who knows how -to- train them?
Monasteries are vastly simpler than kingdoms to run.
What do think scribes did?
Scribes writes down letters (not really hard to do) and keep the annual chronicles and as I have read translated passages from the Frankish Chronicles, I can say it's not complex stuff.
Example; In the year XXX the XX year in the reign of blessed King XXXX, the queen gave birth to a birth to a boychild XXXX, the Danes raided the the Saxon match and after glorious defeating the Danes them king XXXX forced a treaty on them which put the border at the River Weser (translation the Danes won and took the Saxony east of the Weser, but the scribe do their best to spin it as a victory).
The Weser border are a example from the Frankish Chronicles in the wars between Charlemagne and King Godfred of Denmark, where defeat after defeat was spun as victories by the Frankish scribes.
The only reason that you don't see similar Danish chronicles before the 11th century is that the idea had not been introduced to the Danes, and their record keeping was mostly oral.
The point is when you have been introduced to the idea it's rather simple to continue (plus you need too as the oral record keeping tend to be lost, when you adopt written chronicles) and you don't need complex financial records which is the hard part, as the societal structure was feudal.