Quick Flat Colours (Patreon)

Duplicate the lineart Layer

2 options - 

I'm so used to this that using a layer clip is quicker for me

So you add a new layer with the layer clip option checked. Fill with white and merge down. Alternately you can fill with the colour of the bg. Sometimes the white can show through a little when you're filling with dark colours

Option 2 is to go into the brightness and pump it right up until the lines turn white.

Then use the paintbucket to fill in. Your lineart will need to be closed and any sharp corners will still leave white dots but its still way quicker than working section by section.