If we come in on the train and aren't checking into a hotel there, are there luggage storage lockers?
From my research (I’ve never been but am on my way!) there are lockers in Flam next to the Visitors Center. Self-service. You can find more info on Norways Best website.
Given we're talking about we-hate-cash Norway, I think it's very likely those lockers will take payment by credit card, but I encountered lockers in a Norwegian train station that were cash only. I had to scramble a bit to find appropriate coins. I don't remember the exact cost, but I imagine it was at least 50 NOK, and I wasn't in a place as touristy as Flam.
Thank you all this was helpful