The Flailsnails multiverse is distributed and lacks any central authority. It is comprised of numerous, only partially compatible settings, that have drastically different economies. Firearms or even more advanced weapons are available in some worlds, whereas obsidian edged clubs might be cutting edge technology in other places. Whereas part of the effect of this is that the Flailsnails agglomeration as a whole takes on the qualities of the strangest and most extreme of the constituent areas, it does leave open to question: what areas does any given PC have access to at any given time? The conventions themselves are largely silent on this topic, but I have been following some informal rules of my own with my Flailsnails PCs that feel fair to me.
Currency conversion. Any XP-equivalent currency in terms of purchasing power is transparently converted between realms. So dollars become LotFP SP become gold doubloons become interstellar credits. Or whatever. Unless a particular physicality is important (such as using silver pieces to craft a crude silver weapon to damage a lycanthrope), in which case you are going to have to have a conversation with whatever referee and figure it out.
Downtime actions and equipment purchasing. I only allow my PCs to buy items or take actions within the last setting visited. This means that if my character is not in, say, Kalak-Nur currently, I need to play in another Kalak-Nur game before I can buy stuff there, even if I have played there before at some point. The same goes for administering land holdings or anything else that requires access to some world-specific resource.
Character-specific abilities, however, are a different matter. If I make a Holmes magic-user, I will craft scrolls at 100 GP per spell level between sessions, even though a particular session referee might have scroll creation work differently within a given setting.
While there is no particular reason why anyone else needs to follow these “rules,” I think they are good guidelines, and also provide adventuring motivation (if you assume that you need to survive a session in wherever before you can buy stuff there). Of course, I also happily apply my own rather stringent encumbrance rules (1 item per point of strength) to all of my own Flailsnails PCs unilaterally, so it is possible that I derive more utility than others from self-imposed limits.