You'd first have to ask, "what level of significance do I need to detect with my experiment?" and, "what is the expected noise level in my response variable?" Once you have those two bits of information you can use the Power and Sample Size calculator ( in JMP 13 this found under DOE > Design Diagnostics > Sample Size and Power). You can learn more about how to use the calculator in the books that come with JMP (Help > Books > Design of Experiments Guide - you want chapter 17 for the calculator). There is also a chapter on Mixture design which might also help address your visualization question in your other post.
Most of the time the number of replicates will be determined by budgetary constraints, not statistical ones. The Power for a mixture design is a bit convoluted because the factors are not independent. Often the goal of a mixture design is prediction, so I would recommend using JMP's Evaluate Design feature to look at the Prediction Variance Profile, the Fraction of Design Space Plot, and the Estimation Efficiencies. You can quickly try different numbers of replicates and look at these features to see how they change and settle on the number of replicates that provide the best balance of budget with predictive ability and model estimation.