Wow I wish I checked this site more often than I do...
Ok, yeah, this is really complicated - I think moreso than I realized when I wrote it. I'll try to answer your questions but I don't know if I can answer them all fully.
If Lavos reunited with the Mammon Machine's Frozen Flame in the original timeline, why does he try to reunite again in the modified timeline? He already has a version of the Flame, another version would just get time-bastardized. Plus the attempt is so dangerous that it's not worth the effort (and the attempt did indeed fail in the modified timeline).
Speaking of Time Bastard, if the Frozen Flame entered a pocket dimension in the first timeline, shouldn't it disappear in the second timeline instead of entering another, different (?) pocket dimension?
I hope I'm understanding this - so you're asking why did Lavos try to reunite with the Frozen Flame again in the modified timeline of Chrono Trigger, right? If you are, this would be my reasoning behind it - think back to Time Error, where Crono & Co. are moving along a 5D "axis of time" where 4D time as we know it is held constant like points on a coordinate plane. So, what we're seeing in the events of Chrono Trigger isn't really Lavos attempting to reunite with the Flame again, but Lavos' first attempt to reunite with the Flame. I could be wrong here, but I think that's the best way to think about it. I'm not sure exactly how Time Bastard will come into play here - the timeline where Lavos is reunited with the Frozen Flame could have just been sent to the DBT time instead, but I don't know what really happened there.
As far as Time Bastard in relation to the Frozen Flame's pocket dimension goes, I'm not sure it can be applied that way. Again, I'm thinking back along the lines of a Time Error approach from Crono & Co.'s perspective, where in the normal timeline the Frozen Flame would have become one with Lavos again. This would mean that in the normal timeline the pocket dimension created by the Frozen Flame would have dissipated or would have been absorbed into Lavos' pocket dimension. In the modified timeline, this doesn't happen, so the Frozen Flame stays in its pocket dimension.
Also how was Lavos reunited with the Flame? Lavos dies in CT but the Flame doesn't follow him in the Darkness of Time, so it wasn't really united right?
Right. In CT, Lavos wasn't reunited with the Frozen Flame after Crono & Co. intervened (assuming the Frozen Flame actually was where I hypothesized it was). In the original timeline, Lavos was never sent to the DBT, and the Black Omen never rose from the ocean. These two things point to a conclusion that Lavos was united with the Frozen Flame after the Ocean Palace disaster in 12,000 B.C. in the original timeline, but not in the modified timeline.
Hope this helps - it's been a long time since I originally thought about this stuff so it's going to be difficult for me to reword the whole theory.