Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019.
(NACA-TN-3781, 1957) is the best available reference (again) and gives a simple rational method for how to account for the presence of cladding.
The reducing in buckling due to the presence of cladding depends on two ratios:
For different loading conditions and stress level the following terms apply.
This method is available in this spreadsheet:
Note that in some circumstances, particularly for panels with low buckling allowables, a cladding reduction factor of greater than 1.00 can occur. In this circumstance a maximum value of 1.00 should be used.