The formula E=mc^2 has to do with the mass-energy equivalence, which says that an object's mass can be described by its energy content. If you convert mass to energy (such as happens in the sun, atom bombs. H Bombs, and nuclear power plants) the energy that is produced is immense, per E=mc^2. But that has nothing to do with transporting mass. No object with mass can travel at the speed of light, because it takes infinite energy to accelerate it to light speed. Reason is that the mass of an object increases with its velocity, according to the formula:

where p = momentum and gamma is a factor based on the Lorentx transformation:

Note that gamma approaches infinity as v approaches c. So as the object approaches the speed of light its mass gets larger, requiring an ever larger force to accelerate it a bit more, from F=dp/dt. It takes a huge amount of force to get close to c, and an infinite force to actually reach c. This is why particle accelerators are so huge - they must pump great amounts of energy into a particle such as a proton in order to accelerate it to near the speed of light before it smashes into the target. Clearly a single photon lacks the energy required to accelerate even the smallest nano device to near the speed of light.

Back of the envelope calculation: the energy in a photon can be found from E=hf, where h = Planck's constant and f = the frequency of the light. For a high-energy photon in the X-ray range with f=10^18 Hz, E is about 6 x 10^(-16) J. If you could capture all this energy and put it into a 1 microgram object, you could accelerate it to about 1 mm/s. It would be a very long journey to the nearest star system.