Dear Abhishek, the anwer will be blunt: just no way! Chladni works on plate-like structures resonating to a mono-frequency vibration. The chladni pattern reveals the mode shape, showing how the vibration amplitude is distributed when a modal resonance occurs. The resonance frequency is determined by the flexural wavelength versus boundary reflections, which depends to the invert of the frequency, but not only as the celerity of flexural waves is in itself frequency-dependent (to the contrary of compressional and shear waves). Nothing from the vibration pattern can determine all the resonance frequency parameters (poisson coefficient, thickness, young modulus...)
As stated above by Dr. Garnier, it is not possible to determine the resonance frequency just by taking a look at the pattern in a Chladni experiment. You will need to know some geometric parameters and material properties of the vibrating plate. The classical Chladni experiment is carried out on a plate with free boundary conditions, which usually is not a trivial problem, although a discussion on the subject can be found in the classical book by Leissa.