How would doubling the concentration of crystal violet affect the reaction rate?

Actually the rate of reaction can be shown as:

R = k [A]^x [B]^y

The rate of reaction can be determined with help of order of reaction which is an experimental quantity and the order can be determined experimentally.

Hence for the rate of reaction crystall violet depends on order of crystall violet and mostly the order of crystall violet is 1 and thus on doubling the concentration, the rate of reaction gets doubles.