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1. To begin to burn. Don't worry, the tinder will flame up eventually.
2. To begin to burn more intensely. The fire suddenly flamed up and crackled even louder.
1. [for something] to catch fire and burst into flames. The trees flamed up one by one in the forest fire. Suddenly the car flamed up and exploded.
2. [for a fire] to expand and send out larger flames. The raging fire flamed up and jumped to even more trees. As firemen opened the door and came in, the fire flamed up and filled the room.