‘Flame point’ is an alternative name for red point while Himalayan is an alternative name for a long-haired Persian. A flame point Himalayan is a red pointed long-haired Persian cat as shown in the photographs below:
Sometimes people shorten ‘Himalayan’ to ‘Himmie’. The term ‘flame’ is only used instead of red when it occurs in the colourpoint pattern. You’ll see flame pointed Siamese cats too. You know that all Himalayans are pointed cats in a very wide range of pointing colours, red being one of them.
When the extremities show red and orange tabby markings the cat is called a Flame Lynx Point. The coat in pointed cats is temperature sensitive. Cooler ambient temperatures can force the parts of the coat other than the extremities to become darker. The reason why the extremities of the body are darker is because they are cooler areas i.e. the nose, distal parts of the limbs, tail and ear flaps. You’ll see some pointed cats with rather poor pointing i.e. limited. I believe this is due to poor breeding.