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Maybe someone with experience in the field of communications and space can clarify my doubts: how we can improve the flow of data transmission to Earth? Imagine a string of satellites that communicate with each other so that the message reaches the earth faster distributed way. Now it seems that communications between satellites and Earth are slower and it has greater delays.

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Maybe I'm not understanding your question, but adding intermediate satellites/probes wouldn't improve the speed of communications. The limiting factor is the speed of light. Adding additional hops in between would just add a slight processing delay, but definately not change the overall latency. Voyager is very far away and it's going to take a while to talk to it no matter what you do.

Subspace relays!

Just kidding. But more seriously, intermediate satellites could possibly improve the transfer rate of information by acting as signal boosters. However, they would have to span substantial fractions of space between points to be useful. We only have a few spacecraft between earth and voyager. I.e. new horizons boosts voyager's signal back to earth (cassini maybe?). And in voyager's case it's probably irrelevant given how old the hardware is and how weak the power source has become.

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