What you have described is a lauch system for surface to surface cruise missiles, not surface to air anti-aircraft missile. Tomahawks, and Harpoons for that matter though they are fired from torpedo tubes, fly at low altitudes. Usually only a few hundred feet off the surface. As such they are harder to locate, harder to hit, and pose absolutely no threat to aircraft of any kind.
Neither missile requires targeting assistance from the sub, while a surface to air missile would. Your claim of some sort of sub-launched SAM still makes zero sense for all the reasons I mentioned earlier.
Why do that? I don't know, but maybe so that the search radar and the missile come from different directions. Harpoons have been test fired from canisters, and that allows the sub to at least vacate the immediate area prior to launch, and also to allow launch from depth.
The idea is just about as wacky as the 747's 'zoom climb,' but there were many witnesses that saw a flare or other light rise up from the surface of the water.
If not a missile, then what? The offical explaination is that TWA 800 lost it's nose after the CWT exploded, continued to fly at 500+ mph with no center wing box, climbed 3,200 feet in altitude, all without the wings instantly snapping off.
So in the end I suppose that a sub launched SAM is about as implausible. I find it improbable but not impossible that some sort of accident occured and was covered up by the Clintoon administration. However, the CIA 'zoom climb' I do find absolutely impossible, and that leaves trying to explain what so many witnesses saw.
UFOs, most likely.