Given a pair of entangled photons (A, B) with opposite spins. Is it possible to opearate on A, and flip its current spin without leading to entanglement breaking (as we are not doing any measurement, I think we would be ok). If yes how does it effect the spin of B?
To answer your question in a correct way I have to rephrase your question a little bit.
The spin of electrons has to do with the electrons magnetic dipole moment and to introduce such property was neccesery after it was clear from observations that the two possible electrons in the same atomic orbital have one more property, called the electrons intrinsic spin. This spin is related to the electrons magnetic dipole moment.
The spin of a photon is something very different and has to do with the two possible alignements of the photon's electric and magnetic field components. As you may be know this field components are perpendicular to each other and both perpendicular to the direction of propagation:
As you can see, there are two (and only two) possibilities how this field components (B for the magnetic field and E for the electric) could be aligned. This is comparable to the fact, that we have a left hand and a right hand and indeed you can use your thumb (k), second (B) and third (E) finger to point in the possible directions of propagation and the field components.
So instead of using the word spin it would be better to use the property of polarisation (in case of photons). One has to ask yourself how you will measure the spin of a photon. What is possible is to measure the polarisation. Entangled photons can be produced using quantum dots. But until now (and this is good for Quantum cryptography the direction of the electric field component of the one photon is equally distributed around 360°. For example it is directed to 120°, than the electric field of the second photon is directed to 120° + 90° = 210°.
Now it doesn't matter how you influence the second electron the first stays uneffected. This is a problem in quantum cryptography because any influence of the environment on photons destroy the entanglement. This happens not only of you flip the polarisation but for any angle of rotation. And since the outgoing direction of polarisation is coincidentally but the filters on the receivers have to be placed in one fixed orientation it could happens that for the same starting orientation the photons go through the filter or not.
Short answer: If you influence one of the entangled photons, rotating his polarisation direction, the direction of polarisation of the second photon stays uninfluenced.
It is possible to flip one particle's spin in an entangled pair but that does not effect the spin of the other, only the correlation between the two.
For example if you have two particles in a Bell state that means that if you measure any of them individually you will find it spinning up or down with 50-50% chance. But if you measure both of them, you will find that they are not independent: they are either spinning the same way or the opposite way (depending on which Bell-state we are talking about).
Flipping the spin of one of them means you go from a 50-50 chance to another state. This is not detectable if you measure either one of the spins, you will only notice that you went from one Bell state to another and thus from correlation to anti-correlation (or the other way around) if you measure both of the spins.
In short: you cannot send superlumial signals this way but you can use it for superdnese coding.