To radiate is to give off energy (usually heat or light) in waves from a central point. It can also mean to move out from a central point in a radial way.
Ex: Everybody knows the sun is necessary for life on Earth because it radiates the heat and light we need to live.
Ex: Students first started moving into the eastern district of the city in the 70s, and since then they've been radiating out from there, moving into houses and apartments all around the original student zone.
Radiation is the movement of energy in electromagnetic waves, such as the kind of energy that comes from an x-ray machine or an atomic bomb. Something that radiates, or gives off light or heat in waves, is radiant. A person who is very beautiful and/or happy can also be called radiant.
Ex: You must wear lead protection when you have an x-ray to protect yourself from the radiation. It can be very dangerous and causes cancers like leukaemia.
Ex: When Sherri put on her new, green dress and had her hair done at the hairdresser, she looked just radiant. I've never seen her look so good.
To flash is to give off a bright light very quickly, as a camera does. To flash something is to show it very, very fast.
Ex: After the camera flashed, we couldn't see anything. It was as if a giant rectangle of color was in front of everything.
Ex: When we arrived at the concert, Julio flashed his press pass and we were able to enter right away without waiting in line and go backstage to meet the band.
When someone does something very fast they do it in a flash. We often say we'll be back in a flash when we plan to return quickly.
Ex: I took my computer to the shop and they fixed it in a flash. I'm not even sure they fixed all of the problems because they did it so quickly.
Ex: When Julian went to the shop he promised he'd be back in a flash. He really did make it back so quickly that we barely noticed he'd been anywhere.