There are a few differences between the three.
The phrase "rushed into" can be (doesn't have to be) used for a singular entity and requires the subject(s) actually get inside the target. So the protesters would have to be inside the national parliament's building. This is also the most neutral of the choices.
Neither "swarmed" nor "flocked to" could be used for the singular. The word "swarmed" implies that they stayed outside with hostile intent (like wasps swarming a person), although it does not preclude them from getting inside. The phrase "flocked to" implies the intent is more positive. Whether they get inside or not is not really covered by "flocked to". For that matter "flocked to" doesn't even need them to reach the target since "to" is short for "towards" whereas the other two do require the target to be reached.
I would agree that when it comes to protesters and government buildings "flocked to" would be an odd choice to use unless they were going there to celebrate a recent victory.