Tree has abundant foliage, but no flowers for last two years. Tree is about 4 or 5 years old.
It sounds like it has too much nitrogen. Is it planted near a lawn that gets fertilized? Lawn fertilizer runoff can often cause nearby plants to not flower. Add some bone meal around the tree to boost the phosphorous and try to keep nitrogen heavy fertilizers away from it.
If I have two Spring Satin Pluots, do they need an additional cross pollinator?
Yes, this tree should be cross-pollinated by a plum of a different variety. Japanese plum varieties are the best option. It can set a small amount of fruit without a cross-pollinator, but this will be much less than its fruiting capacity.