I saw this mentioned a couple of places so I figured it was worth talking about.
SPOILERS for Convergence Booster Gold
On one review I read I saw a comment mistaking what's wrong with pre-Flashpoint Booster (a.k.a. Dad Booster) being the same thing that happened in his original series. It isn't although I can see the confusion as Rips' comment about unshielded time travel did remind me of it. In the first BG series Booster got sick because he was from a different time period which made him vulnerable to bacteria in the past. The reason for him not being affected faster being that he was using his force field so much it slowed the process down. This was undone when he was cured in his time period and allowed himself to get used to the bacteria in the present so it wouldn't happen again.
What happening to him now is that he's absorbed too much of the energy used for time travel (*1) I think all time travelers are affected a little bit by this energy as Booster did start to see time changes in his second series. His JL certificate changed into a death certificate for different people in the first arc which only Rip, Skeets and him can see.
This energy is usually used to give travelers powers like Chronos 1 when he made a deal with the devil and for a time Degaton in Johns JSA. It's also used with temporal anomalies as the means to ensure they aren't erased despite having their timelines altered. As seen with Chronos 2, Waverider, and Rex Hunter/Jason Goldstein.
The rainbow energy we see when Dad Booster is in pain/fading? It's seen in the second BG series as the leads travel through time and as Rex Hunter gets "erased" and becomes a being made of this energy. For some reason Dad Booster is connected to the cities Telos set up. In FEBG and CBG he ends up hoping from one city to another. Interestingly the heroes that couldn't use their powers because of the domes can when he's in the city. Those powers disappear when he leaves and only come back when the domes are opened.
What's really puzzling is if all time travelers can be affected like this. New 52 Booster asks if it can happen to him and doesn't really get a solid answer. Rip has been using time travel his whole life which should be more than Dad Boosters' 15 plus years yet he seems fine. He does say that it's due to too much unshielded time travel so does this mean Dad Booster had too many emergency jumps? I think I recall Rip improving the uniform to make it possible for Booster to be safe. Still I can see him doing dangerous jumps to prevent his young son from being assassinated. It will be interesting to see how this is resolved.
*1 I've seen it referred to by a few different names/forms and used for various means. Basically it's used for time travel, to get time related powers and mishaps. I know these stories don't use the same names. This is basically me boiling down these plot threads to their simplest forms in storytelling.