At 34:45 into Crimson Tide (1995), Captain Ramsey (Hackman) is sitting at his desk talking to Commander Hunter (Washington).
On his desk, a small U.S. flag is displayed with what looks like the Icelandic flag.
Is there any explanation for why the Captain would be displaying another nation's flag?
As an additional, a note on the flags present in the movie, so not quite an answer:
OP asks Is there any explanation for why the Captain would be displaying another nation's flag?
As the other answer states, it is probably alluding to previous service with international peers (such as NATO), but... because of inconsistencies with it as a set dressing - Iceland is picked out in the question for example - however in some shots it has completely disappeared, so it could, in fact, actually mean nothing at all.
tl;dr:
So yes, it could possibly be a memento from a meeting, a gift. These are sometimes seen in press photos when personnel from different nations come to meet, like a conference.
As a set dressing:
Early in the movie, there is the first meeting between Ramsey and Hunter:
Flags visible on his desk are for the United States, United Kingdom and the Flag of Washington.
Reason for the Washington flag is likely that in real life, USS Alabama, SSBN-731, had her home port in the state of Washington, at the Naval Submarine Base Bangor, which was one of only two Trident missile submarine bases operated by the USN, this one specifically for the USPACFLT (US Pacific Fleet), and the other in Georgia is for the USLANTFLT. Ballistic missiles for the submarine fleet are stored and maintained here. The base has since been merged and renamed, but that was a long time after this movie was made.
Next we have the video playing of Radchenko in the 104 Records room/100 Operations room (both doors enter into this room) - similar (or the same) mini desk flags are on display here too, on two desks:
The far desk has display stands for up to (at the time) 16 flags for NATO partners, including United States, United Kingdom and Italy. Others, if any, are obscured.
The desk nearest the camera has another display: Iceland, United States, the flag of the United States Navy, and perhaps up to two unidentified flags.
Flag of the USN, with CAVU (Ceiling and Visibility Unlimited, Naval Aviator term)
Then you have the tense meeting with Hunter in Ramseys quarters:
Flag display looks to be for NATO - unidentified red (due to amount of red shown, could be Denmark or Turkey), Italy, United States, Iceland.
Here, as pointed out in the other answer, there are continuity issues:
When this scene ends, the Iceland flag is no longer seen in Ramseys quarters again.
Which then changes again when Ramsey is confined to quarters:
Flag display looks to be: Italy, United Kingdom, Flag of Washington, United States. Other than Italy, this looks to be the same display from Hunter and Ramseys first meeting at the beginning of the movie.
Further caps of the set decoration change in Ramseys quarters:
Finally, aside from Hunter and Ramseys tense meeting after the fire and drill, what is perceived as continuity issues might just be Ramsey messing around with his desk displays at different times of the day. Maybe, he really likes his little flag displays...
Additional:
Regarding Iceland in particular, although the flag is seen, a nuclear submarine did not dock in Iceland until 2025.
USS Newport News, SSN-750, was the first USN nuclear submarine to dock in Iceland, July 2025:
Up until then, (outside of the air base) only its waters were used for naval activities such as refuelling and exchange purposes, all at sea, but no nuclear submarine had ever docked there. Also Iceland does not have a standing military - it carries out its operations through its police forces and coast guard instead.
Given the above, and the presence of other NATO member states flags present in the movie, its probably less just Iceland and more to do with NATO.