No-one else commented on this so I have researched it and it seems that 'Jag skyndar mig.' means I hurry, and 'Jag skyndar på mig.' means to hurry up or get faster (at whatever is referred to), ie bring about an increase in the tempo.
Well I'm English and hear the verb 'to hurry' used as a reflexive verb very often. "I am hurrying myself along", "hurry yourself up" etc. Might be dialectal, but I've heard both my northern father and my central mother use it.