Multiple start flexures are beneficial because they not only provide redundant elastic elements should a failure occur, but a failed element (coil) will be physically trapped by the remaining ones.
A multiple start compression or extension spring is balanced when a load is applied, which prevents tipping. Traditional wire springs and single-start machined springs have an unresolved moment when a load is applied. A coupling with a multiple start flexure will have a stiffer torsional rate and can transmit more torque compared to a single start flexure.