I am providing this answer considering myotatic reflex arc (as you have specified in the question).
There are so many factors on which it depends...I have listed as many as I could -
Here the sensory receptor is intrafusal muscle fibres. Afferent neurons are type Ia or type II. Central processing may involve mono- or poly- synaptic junction(s). Efferent neuron is alpha or gamma motoneurons. Effector is intra- or extra- fusal muscle spindle.
Considering the human or animal to be of normal health and condition (absence of hypoxia, pyrexia, high or low pressure and anesthesia) sensory receptor takes the shortest time in reflex arc. Central synaptic junction may be mono- or poly- synaptic. Poly-synaptic junctions take longer time, but still it is shorter than neuro-muscular transmission.
So the competition now is between neurons and neuro-muscular junction. In case of neurons it mainly depends on the length, diameter and myelination (provided the above mentioned conditions about the sample is "normal"). Neuro-muscular transmission speed depends on the length of synaptic cleft, body calcium and chloride level, type of muscle fiber innervated and the type of reflex arc (alpha-gamma co-activation, reciprocal innervation etc) to name a few. So, it can be said that longest time would depend on the reflex arc you are considering, as this will decide the speed of transmission through the afferent and efferent neurons and neuro-muscular junction.