How to obtain the exact value of wavelength from a 2D FFT amplitude vs wavenumber plot like it is obtainable from 1D FFT amplitude vs wavenumber plot?
First, you want to find the peaks in this 2D plot. In your case, you know that there will be 2 peaks in your FFT (because you added two sines). Your plot shows 4 peaks because the FFT magnitude is symmetric, since your signal is real. You can discard negative wave numbers and look for peaks among the positive wave numbers.
The wave numbers corresponding to those peaks belong to your signal. There will be two wave numbers corresponding to each peak, $k_x$ and $k_y$. We know that $k = \frac{2\pi f}{c}$, where $k = \sqrt{k_x^2 + k_y^2}$ is the wave-number, $f$ is the frequency in Hz and $c$ is the speed of sound in the medium. Now, using $\lambda = \frac{c}{f}$, we can deduce that $\lambda = \frac{2 \pi}{k}$.