I work out depending on mood 3-5x a week, as a bodybuilder. I've come close to competing but always end up with some diet fail not too long out from a competition where due to vacation or work travel I eat too much and add to much fat to get lean enough before the show.
I don't think particularly bodybuilding has a ton of value, although I doubt it hurts. Being able to curl 60lb dumbbells vs 25s doesn't make a load of difference in your shot either way. For the really huge bodybuilders maybe there would be issues with just getting into a good stance or positioning.
The 2 areas where bodybuilding or other kinds of exercise could come into play are endurance and central nervous system response. Endurance is easy to understand, pool is more physically stressful than people would guess, and playing for 2 hours straight through can definitely take it out of you. So raising your overall endurance could definitely help.
As far as central nervous system, its a little more of a grey area in terms of the best ways to train it. Its value on the pool table is slightly in anti anxiety, but also in being able to maintain that high heavy concentration level for each shot. This is the area where bodybuilding or powerlifting style weightlifting can probably do a little more than other exercise in that they both train the CNS to handle progressively higher loads over time and also given the amount of time spent training you build CNS endurance (which is a bit separate from general physical endurance). Really only way to get that sort of stimulus from other exercise forms is to be pushing them to the edge. Running a couple miles wouldn't do it, marathon training would. Its the push to the point of failure that is what is most responsible for gains in that area.
And as far as weight training hurting flexibility, that is only if you work out like a meathead and don't do flexibility work

Its definitely possible to retain flexibility while doing it, but you have to be thinking that way from the start.