I don't recall reading anything about using for correlation estimation. It's an interesting idea. But the KF isn't really a prediction tool, as such. So it isn't like using a GARCH model to forecast volatility for option pricing, for example.
What KF does is provide a way to estimate the true (unknown) state of a system when the measurements are noisy. So, for instance, it is used in satellite positioning systems and also in hand-held devices like smartphones: you want to know as quickly and accurately as possible what the true position of the phone is, given some noisy measurements from the gyroscope and accelerometer. KF can help with that.
Whats the application to pairs trading? Suppose there is a relationship between two stock prices A and B, where B = A * beta. So you have noisy estimates of the true underlying relationship beta = B/A. KF tries to minimize the noise and maximize the accuracy of the estimate, so you can identify misalignments in the relative pricing of A and B.