The hardest part is going to be getting Novgorod in this union. The easiest part is getting Scotland and Norway unified. There were already opportunities IOTL for that to occur by marriage. There could also feasibly be an invasion by Norway under some pretense or another which leads to them conquering Scotland, assuming they had some good luck on their side. Iceland and the other mentioned islands should come with those two crowns, and the next part is harder. Norway is not likely to invade Finland by itself, they would much sooner target Sweden or Denmark. Sweden and even Denmark are also far better positioned to take Finland than Norway is.
Theoretically however, you could have Swedish nobles based in Finland gain independence and have their own kingdom of Finland that would partake in eventual crusades in the Baltics and take Estonia, though it would be quite difficult and require a lot of luck*. Then, if you have them intermarry with the earlier mentioned Scotland-Norway, you could get Scotland-Norway-Finland, with most Sami lands drawn into their orbit naturally. Then the hard part is getting Novgorod, which is strong enough by itself to crush the union and take Finland for itself. The best way to avert this is to have the Swedes take Novgorod when they take Finland (this is unlikely, but possible if they have some military geniuses on hand while Novgorod is lead by morons), and for Novgorod to be the main powerbase of the Kingdom of Finland when they get independence from Sweden. The issue here is one of religion, since Novgorod being thr main powerbase of Finland would lead it to likely turn Orthodox, which would likely ruin the chances of Finland getting inherited by some king of Norway and Scotland. The best way to avert this is to have the union occur early enough that Finland has not yet turned Orthodox, though it does appear that the schism did not stop intermarrying between Scandinavian kings and the Rus until centuries later.
However, Norway-Scotland-Finland's interest is likely going to be to get Sweden and Denmark, so what would likely need to happen is Sweden and Denmark being strong enough to hold off the NSF union, but not strong enough to dissolve it. But the union is very unlikely to last, simply due to logistical issues. Either the "Finns" will want independence again, or a neighbor is likely to end it at some point.
*becomes easier with the assumption that Novgorod is part of the Finnish kingdom, but potentially screws the timetable for Finland to get into the union to begin with, unless Sweden conquers Estonia prior to Finland getting independence, with Estonia being part of Finland when it gains independence.