How are reflexes suppressed?
Short answer
The pain withdrawal reflex can only be suppressed when touching something painful on purpose. Deliberate, conscious contraction of the extensor muscle before reflex initiation can prevent the contraction of the flexor muscles once the reflex is started.

Background
The pain withdrawal reflex arc (Fig. 1) receives input from sensory neurons that enter the dorsal part of the spinal cord via the dorsal root of the spinal nerve and synapse onto interneurons within the spinal gray matter. The interneurons in turn synapse onto motor neurons, which send axons that exit the cord via the ventral root. They conduct information to the muscles. The resulting withdrawal reflex is initiated by activating motor neurons of the flexor muscles (agonist), and simultaneous inhibition of the motor neurons to the extensor muscles (antagonist). This loosening of the antagonist while the agonist is being contracted is referred to as reciprocal inhibition (Crone, 1993). More important to the question is the fact that the motor response is well under way before the signals responsible for the conscious sensation of pain (which exit the reflex pathway in the spinal cord) ever reach the brain (Cornell University).


Fig. 1. Schematic of the pain withdrawal reflex arc. Source: Washington Uni. 

Hence, the reflex pathway is initiated even before we are aware of any pain. The only possible way to suppress a reflex that is faster than perception is to start counteracting the agonist (flexor) before the reflex is initiated, i.e., by contracting the antagonist (extensor) before touching the painful object. 

Reference
- Crone, Dan Med Bull (1993); 40(5): 571-81