How capacitors connected in series are affecting the total capacitance of the network, since there is no actual flow of electricity due to dielectric?
It's quite simple really:

One plate of the first capacitor is negatively charged - that is it has excess electrons.  Those electrons repel the electrons in it's opposite plate.

Those electrons have to go somewhere, so they go towards the first plate of the second capacitor - so that plate then has excess electrons, which then repels the electrons in the second plate of the second capacitor.

And of course those repelled electrons have to go somewhere ... ad infinitum.