I don't believe JMP has a direct calculation for KMO. I'm sure someone will correct me if I'm wrong. You can do it yourself with some effort. Under Multivariate you can produce Correlations and Partial Correlations and then turn them into data tables using Make Into Data Table. Then you can manipulate them manually or via scripting to calculate KMO from its definition.
Alternatively you can assess collinearity by looking at the VIF values. They can be gotten from the Multivariate platform by asking for Inverse Correlations. The diagonals of this matrix are the VIF values for the associated variables.