It is very common to experience a faster heartbeat during a flush. Hot flushes can be caused by an adrenalin rush, and this will also cause rapid heartbeat. Herbs such as Passiflora may be useful for this symptom, and a magnesium supplement may be a good idea too. However, if you are at all concerned by this it is a good idea to get it checked out by your doctor.
It is difficult to say how long this will last for, as it is a very individual experience, but learning to relax is really important. Spend 30 minutes a day on it if you can - deep, slow breathing can often help to reduce the severity and frequency of hot flushes.