It is true that Russian surface-to-air, anti-ship, and surface-to-surface missiles in Kaliningrad pose a threat to NATO reinforcements flowing into and through Poland or in the nearby Baltic Sea:
There are significant military bases for air and ground operations and for surface-to-surface cruise missiles. Kaliningrad is also important from a naval perspective, as it is Russia's only year-round ice-free port on the Baltic.
The level of new military construction activity in Kaliningrad was recently exposed at the unclassified level, with reporting that included significant analysis of commercially available overhead imagery. Russia is increasing its overall storage capability at the major depot for tactical nuclear weapons. At Primorsk, the key naval base, it has constructed 40 new weapons bunkers. And at Chkalovsk, the main air base, major aviation and weapons-storage improvements have been made, including to the storage sites of Russia's highly sophisticated (and highly controversial) Iskander short-range missiles, operated by the 152nd Missile Brigade.
But Russia defends this exclave with just 3 army brigades and a contingent of marines. Russian brigades are significantly weaker than American-style brigades. Until Russia wants to risk a lot more troops to hold the exclave and commit to a major offensive through Belarus and other Lithuania to hit the Polish Suwalki Gap, the exclave is vulnerable to running out of weapons and ammo if cut off and attacked with fires (it is small enough that NATO ground fires could knock out air defenses, clearing the way for adding air strikes to destroy the other missiles); and vulnerable to a NATO ground offensive to take the territory.
That NATO offensive should be a primary early mission if Russia starts a war over the Baltic NATO states. That would eliminate the missile threat, eliminate a potential anvil at the western side of the Suwalki Gap for a Russian hammer striking from the east, and provide NATO with a bargaining chip to regain and Baltic territory still in Russian hands when a ceasefire is declared.
Remember that NATO held the far smaller West Berlin in the Cold War with three strong brigades from America, Britain, and France. Yet there was no hope that those forces would be a threat to Soviet forces--just a speed bump that could hopefully occupy the attention of Soviet bloc forces and interfere with the line of supply for as long as possible while the main fight took place in West Germany.
Yes, if Putin puts nukes in Kaliningrad there is a risk that Moscow might believe they should use them or lose them. Although they would be a small portion of Russia's nuclear arsenal so it wouldn't make sense--but with nukes logic may go out the window.
So a NATO ground offensive that avoids taking that precise location of the nuclear warheads and instead drives the Russian defenders into a small perimeter that eliminates their anti-access/area denial (AA/AD) threat to the region around them would be sufficient to secure the NATO flank.
