Perhaps I am mistaken but I do not think silica is significantly soluble in chloroform whether or not there is some added methanol(or ethanol). However I think such a solvent may very well more easily suspend silica nanoparticles. The refractive index of chloroform is quite close to what you would expect for a silica suggesting the possibility of reducing the effective dispersion force between silica particles when suspended in chloroform.
I do not know of a mechanism by which chloroform or ethanol could cleave the Si-O-Si bonds. Water on the other hand can hydrolyze them.
Si-O-Si + H2O => 2Si-OH