There is only one account of Vikings tying boats together in battle, and that is in the battle of Svolder. The boats were not burned, so there are no records of this Vikings burning a "ship island".
That's the actual answer. The rest here is a somewhat speculative expansion:
Tying your ships together is a defensive tactic, used because you can in practice only board a ship from the side. By tying his eleven ships together side by side, Olaf Tryggvasson in practice only needed to defend his two outer ships, evening the odds when you are at a numerical disadvantage.
But it also leaves you in the situation that you can't move and attack your ships. You can not therefore, as you seem to imply, have two sides each with a "ship-island". You would end up with two un-navigable islands, and it would have been hard to attack each other. :-)
So if an attacker finds itself unable to make any inroads onto this island of ships, why don't they just burn it down?
Well, there are probably several reasons. One is that putting a boat on fire isn't that easy, there is plenty of water around to put out small fires after all. That's why Huang Gai uses fire ships. This means that to burn the enemy, you have to in practice set fire to one of your own ships, and somehow sail it into the enemy fleet. That requires that you fill a ship with kindling, and is nothing that is done in the spur of the moment, but need to be prepared beforehand.
The second is that the ships are not actually that much more susceptible to fire because they are tied together. I can't find any reference to that any boats were tied together in the Battle of Red Cliffs, for example. The problem is rather that they aren't ready to sail away, and so have no means to avoid the flames and sparks. But this is difficult in a sail ship at the best of times, even for the attacker, so there is some risk that you put your own ships on fire, unless you withdraw completely before you bring in the fire ship. But then you give the enemy room to untie the ships and sail away, or worse, turn and attack you.
So while putting the enemy fleet on fire have been successful in some cases, I don't think it is a common defensive move.