1. double clutching is something you (used to have to) do on downshifts with gearboxes that have weak synchromesh - like the JC5 in Clio Sports - or didn't have synchromesh at all - like trucks and race cars. You push the clutch in, move the gear lever to the neutral position half way to the next gear, let the clutch out and blip the throttle, then push the clutch back in and move the gear lever into the lower gear. What that releasing the clutch and blipping the throttle does is speed up the gearbox input shaft so its matching the speed that it has to be spinning at for the lower ratio you are going into. These days even trucks have good enough synchros to not need to do it, and racing car gearboxes are either strong enough, have synchro or have motorcycle-type dog clutch gearboxes. You shouldn't need to do it on any modern car unless its got a faulty gearbox. The need to double-clutch in trucks led to some really scary situations. You'd find yourself on a steep downhill with a heavy load, and the brakes'd start fading, so you try for a lower gear to use engine braking to help. But the truck'd speed up when you went into neutral and when you went for the lower gear it'd be going too fast and wouldn't go in. And the more tries you had the more it speeded up. That's why they have those warning signs telling trucks to select low gear now at the top of steep downgrades.
2. flat-shifting - leaving your foot flat to the floor on the accelerator - is something you do on upshifts. Its scary to do if you don't have rev limiter, but virtually all modern cars do. With your foot flat on the accelerator and the clutch in the revs rise, and that gives you are bit more acceleration when you let the clutch out again as the engine gets dragged down to the right revs for the higher gear. Its also called a racing change. Its something you only do when you're racing.