Is it possible to reveal a slight chronological change in frequency of Voyager 1 and 2 signals due to Hubble flow effect?

No. There is a Hubble flow, but no Hubble flow effect, i.e., nothing that makes objects tend to move with the Hubble flow. Matter moves in that way on large scales because some historical process (perhaps inflation) gave it that velocity distribution 13.7 billion years ago. Some of that matter later collapsed into the Sun and Earth and so on. Voyager 1 and 2 were launched from Earth with known velocities into a known distribution of matter, and their motion since then is purely due to their interaction with that matter. There is no extra effect from the process that ended 13.7 billion years ago.

I wrote another answer that covers this in more detail.