There's a man made MTB descent for advanced riders that runs from La Flegere to Les Praz. Take the La Flegere cable car to the top station at 1800m. Upon exiting the lift station, turn left taking the steep 4 x 4 track that runs through the trees back down to the valley floor. Although the trail is purpose made for bikes, Compagnie du Mont Blanc made the decision to focus on bike infrastructure at Les Houches and Le Tour so this trail has not been maintained since summer 2012, expect fallen trees and large rocks strewn around!)
For the other more advanced trails consult a local guide or use the excellent locally produced “Chamonix Bike Book”
The terrain around these lifts includes the Aiguille Rouge Nature Reserve which has restrictions on use by various groups, including mountain bikes and dogs, so make sure to check you aren’t straying into the reserve if you’re planning a long ride.