Can angels travel at the speed of light? Yes would be the correct answer. Consider that radiation travels at the speed of light. Radiation is energy and we can understand this when it hits our skin and causes a sun burn. When light waves travel through space they are potential energy. When these light waves hit a object they become kinetic energy and burn the object such as our skin. Therefore consider this, angels are potential energy when they move through space at the speed of light, or greater. But when they hit the atmosphere of a plant they become kinetic energy, which causes them to be observable by the human or alien eye.
Radiation such as the light we use to see, travels through space in a vacuum or near vacuum. It travels at the speed of light, which is approximately 186,000 miles per second. However light and other parts of the spectrum, such as UV radiation has no mass. So theoretically these forms of energy could travel faster than the speed of light, which is an astounding 300,000 km per second. Light waves traveling at any speed would have no mass and no momentum. Consequently no energy would be required to start their motion and accelerate their speed. In fact to get radiation to reach 300000 km per hour would be instantaneous.
We see the vastness of the Universe when we look into the night sky. The unlimited number of stars and galaxies are arraigned before us. Astronomers tell us the universe is so large it takes the light form the most distant parts to reach us in millions of years. In fact when describing how far away the most distant object is from Earth, the term light year is used. The term light year refers to the distance light can travel in one year. Yet angels can travel this distance in an instant, no time at all, as they can exist outside of our Universe. God created the Universe. God most certainly can travel anywhere in our Universe in an instant or in zero time. The time spoken of here is how we think of time.
God and the angels are not flesh. When they travel through our Universe they are energy, what we understand to be potential energy. Yet we fully cannot understand their energy. It is written in Exodus 33:20 "No man may see me and live". They transcend our fleshly existence. They can travel beyond the speed of light and their movement is instantaneous relative to our motions.