I do like the emergency exception. The problem then becomes having a solid policy on when to use it.
Not really sure about the flakiness test (the 25% figure is totally random), as you could have a test that is failing only at a certain hour of the day and you would be furiously rerunning the test suite for nothing because it would always fail, wasting resources. It would be much better to at least single out the failing tests and rerun only those, dropping the ones that pass successfully until max tries are reached or the queue is empty.