Yeah the whole Flashpoint thing was very much 'Look we have Swamp Thing and Constantine again!' rather than making any actual sense. Especially didn't make sense as they both appeared in Brightest Day stuff just prior to Flashpoint.
So I guess if you wanted to rationalize it you could say it was just an emphasis in the panels on those DCU characters being emphasized/important again.
Personally I'd just ignore it, Vertigoverse was an entire multiverse unto itself anyway and is better being a similar but detached thing to mainstream DCU.
Oh I know they were meant to, it's just that stopped making sense around the mid 90s, when Vertigo people aged normally and DCU worked on comic time. And then when the Vertigo stuff continued with Lucifer, it came up with it's own backstory and stuff that didn't gel at all with the DCU at the time.
Idk take it as you will, but I got to the point where I just take the Vertigo stuff as a similar but unconnected Multiverse to the mainstream DCU, with the event where they diverge being Moore's Swamp Thing.
It's basically what DC is doing to their mainstream universe. Not everything is connected (See Geoff Johns JLA to Snyder's Batman), because each has it's own story, but everything is within the DC realm of the multiverse. Lucifer would still be part of the DC Omniverse.
And I really like the fact that Holly Black has clearly gone over Lucifer/Sandman etc to work out how to continue this. I mean in the first issue she addressed Gabriel's Fall, Mazikeen, Lucifer's lack of power & his meeting with Yahweh in the void and mentions Elaine so I imagine that will come back into play at some point.
I mean there's still something a bit off with Lucifer's voice but it's issue one and I'm actually intrigued who killed God. And I quite like the way they did it- a hole in the Primum Mobile.