Does the damage of poisoning amplify with each use? If I got a Bonus Action on a Puffor and used Plague would it inflict more damage than just one Plague?
No it won’t. Because poison is calculated overtime. Therefore if you have BA, the second one still starts at the same time (TU).
Are you sure about that ? sometimes with octoneer I get 2-3 BA but due to TU I need to use his poison (100TU ) and I notice that after 3 poison in a row opponent take more poison damage (ex: If I use 3 poison attack, life decreases as if the 300TU have passed). But maybe this was in my head 
or visual…
I’ve noticed both happening. Sometimes the HP will decease, albeit minimally, while sometimes it won’t. I’m not sure which is “correct.”
Maybe one of the mods know?