This slang likely originates from the portrait of Alexander Hamilton on the $50 bill. While Hamilton was born in the British West Indies, his family later moved to New York, which was a Dutch colony at the time. Finland, a Scandinavian country, was also once part of the Swedish Empire. This loose connection to the Dutch and Swedish connection could have inspired the slang term "Finn" to become associated with the $50 bill.
It's important to note that this slang is not widely used and is mainly confined to certain circles, especially in the realm of rap music and street culture.