Every field has its general and specific aspects. Flexibility is a general part of skating as it assists in the performance of almost every trick. And, as I've painfully discovered, without it one can't even perform the most basic manoeuvres. Contrast this with the absence of a more specific ability such as being able to flip the skateboard sideways which doesn't impede the performance of many other non-flip tricks. In most sports, stretching is a standard part of the training and a routine warm up for the sport. Interestingly, however, skaters (excluding vert skaters) don't seem to stretch much - if at all - before skating, even though flexibility helps minimize injury and greatly enhances performance.
Leg muscle strength is another general element of skating as most tricks depend on the ability to jump well. There are two basic types of muscle strength:
a) Explosive: the ability to access one's muscle power in rapid bursts as is clearly visible in the ascending phase of a jump.
b) Supportive: the ability to support a weight for a given period of time. This is apparent when one crouches down in preparation for a jump and the legs support one's body weight in this position for several seconds.
Explosive power largely depends on supportive power because explosive power requires a stable base from which to express itself, a 'launch pad' if you like. Observe professional skaters and you'll find that they have an ability to crouch in preparation for a jump and to hold the position firmly until they tap their explosive jumping power for the trick. Also, when landing, they tend to crouch again in order to absorb the impact. They often maintain this supportive crouch stance for a few seconds after they land back on their board. This is most visible in tricks down sets of stairs.
Overall, muscle strength and muscle flexibility are interdependent as they are active and passive complements. Flexibility means that the body can be shaped - passively - into different postures; strength, the active element, is the force that effects the change in posture and maintains it. Strength without flexibility means that a person has the energy to assume certain postures but is too rigid to do so without injury or discomfort; flexibility without strength implies that one can be shaped into various postures but lacks the energy to do so.