Nothing "escapes" a BH - in the sense that a signal originating inside the event horizon remains forever inside. If something is observed moving away from the BH, then it was generated outside the event horizon. If it was generated inside, it would never be observed at all, forever and ever.
Gravity itself does not "escape" a BH - and neither does "not escape". Gravity is simply a characteristic of the metric of spacetime. If spacetime is warped in a certain way, gravity can be measured to exist. A BH is simply a very powerful distortion of spacetime, nothing more, nothing less. It is generated by a concentration of mass/energy, which warps spacetime, and then that concentration becomes trapped by this distortion that it has produced.
In that sense, gravity is simply part of the BH, because gravity is spacetime being warped, and because a BH is essentially just that - warped spacetime. A BH's gravitational field is part of the BH itself, extending to infinity (but getting weaker with distance). It doesn't "escape" because there's nothing there in the process of escaping.
It's like having a plastic bag tied into a knot to keep water inside, and someone asks "so how does the plastic escape the knot?" The plastic does not "escape" the knot, the knot is part of the plastic.
This all becomes easier to understand when you realize that gravity is not a thing, it's just an effect of spacetime being distorted.
EDIT: I think what you were really asking was - can a BH have its own magnetic field? The answer is yes.
A BH can have 3 characteristics: mass, spin (rotation), and electric charge (a.k.a. the no-hair theorem). All other characteristics of the matter falling in it are lost, except these three. If you drop a proton into a neutral BH, then the BH acquires a charge equal to one proton, and that's a measurable electric field.
Now consider a spinning BH with an electric charge, the Kerr-Newman metric. You have a charge, and you have spin. That means you have magnetism. So, yes, a BH can have a magnetic dipole. However, the rotation axis and the magnetic dipole axis must be aligned - a BH cannot be seen as "pulsing". Again, no signal from inside the event horizon can be observed outside.
However, you should not imagine the electric (or magnetic, same thing) field as "escaping" the BH. It does not escape. What happens is, when the charges were swallowed by the BH, the lines of electric field remain "glued" to the BH, which then acquires a charge. Those lines of electric field have existed forever, they don't "escape" anything, and continue to exist after the charge is trapped by the BH.
Note: electric fields and magnetic fields are one and the same. One could appear to be the other, depending on the motion of the observer.