Protein structure is commonly regarded to be conserved and to dictate function. Most proteins rely on conformational flexibility to some degree. Are regions that convey conformational flexibility conserved over evolutionary time? Can changes in conformational flexibility alter protein function? Here, the evolutionary dynamics of structurally ordered and disordered (flexible) regions are investigated genome-wide in flaviviruses, revealing that the amount and location of structural disorder fluctuates highly among related proteins. Some regions are prone to shift between structured and flexible states. Increased evolutionary dynamics of structural disorder is observed for some lineages but not in others. Lineage-specific transitions of this kind could alter the conformational ensemble accessible to the same protein in different species, causing a functional change, even if the predominant function remains conserved. Thus, rapid evolutionary dynamics of structural disorder is a potential driving force for phenotypic divergence among flaviviruses.