Explain why we did not see distinct lines (like on an emission spectrum) when the metal salts were burned.

Actually when we burn metal salts, we cannot actually really see distinct lines to appear because in reality, they are not really visible to the human eye. There is only a certain range of wavelength of light that our eyes can see.

To state in other way, some metal salts will give off light which has wavelengths that are outside of the visible region of the electromagnetic spectrum.