The chemical energy converted during a muscle contraction is stored in the muscles and is separate from the chemical energy used to fire the neurons which ‘trigger’ the muscle contraction. In this sense no energy from the brain is directly used by our muscle during the contraction.
However, it does take energy in the brain to fire the neurons which start the muscle contraction. It takes a few femtojoules for a neuron to fire (that’s about a billionths of a billionth of the energy in an AA battery). However there are a lot of neurons in your brain, about 100 billion. I don’t know how many of these would be involved in activating a muscle, but if we assume (arbitrarily) that every neuron needed to fire to in order contract a muscle then this would consume 0.1 millijoules, or about 100 millionth of an AA battery.