Log flushes per second appears low
I don't know anything about the Redgate tool you're using, but it sounds like "transaction per second" would include read and write transactions together.  So the likely explanation is that the one database with high log flushes per second is the only one with a significant write workload (thus generating log flushes).  The other databases may have lots of read transactions, but these don't generate any log activity.

Regarding your note at the end, the log activity in the middle of the night is probably due to index maintenance, which is a common thing to do overnight that generates lots of log records.

Without details about your databases, these are mostly just educated guesses based on the information provided in your question.