Well, historical parallels are tripping us up here because in the Middle Ages, you were only considered literate if you knew Latin. Being able to read and write in your native language didn’t count.
The extent to which the lesser nobility learned Latin is a matter of historical debate. Certainly, we know that it was considered unusual and notable that Henry I could read Latin instead of relying on his clerks (hence why his nickname was Henry Beauclerc, or Henry the Good Scholar), but from King John’s reign (1199-1216) onward, royals were routinely educated in Latin. And as Harvey Graff argues, “the example set by the kings inevitably gave the baronage and gentry a motivation to learn some Latin, both to avoid looking foolish at court…and to have sufficient understanding of the written demands” of their king.
How far down that penetrated is hard to say, because evidence is difficult to find. For example, how do we know that documents in Latin from various knights were written by the knights and not by clerks they employed? Best guess is that your average knight knew enough Latin to do their jobs.
As for Ser Barristan, it certainly is a mark of distinction that he can speak so many languages. On the other hand, Ser Barristan was not your average knight – he was born the heir of House Selmy, a principal House of the Stormlands, he served in the Disputed Lands where most of his enemies would have been speaking some form of Valyrian, and he served in the Kingsguard which means spending time in the royal court. So he’s more likely to know a second language than most.
But a lesser landed knight who didn’t rate having a maester in their household? There’s a good chance they’re not functionally literate in the Common Tongue, let alone in Valyrian.
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