So I'm thinking of buying some V-Bucks on Fortnite, Battle Royale mobile. Do the purchases save cross platform?
TL;DR: If you buy V-Bucks on PC or mobile, they are shared if you have your Epic account linked. If you buy them on PS4, Nintendo Switch, or Xbox One they aren't shared. The items you buy with them are shared if you have your accounts linked to your Epic ID. Any earned V-Bucks from playing are shared across platforms.
Interesting enough, V-Bucks have some odd rules. The official FAQ page (Billing section) states:
Purchased V-Bucks are shared between PC and mobile if you've linked your account with your Epic ID. However, V-Bucks purchased on PlayStation 4, Xbox One, or Switch are not shared between other platforms.
According to a post made by Epic Games in regards to PS4 and Nintendo Switch:
V-Bucks purchased on Nintendo Switch and PlayStation 4 are only available on the platform they are purchased on. All other V-Bucks, are available across platform.
So it looks like any V-Bucks you buy on a console are only for that console. Any that you earn from actually playing the game are cross platform. The article states that this restriction applies only to the V-Bucks themselves. The items you purchase with them are cross platform (if you have your account linked to your Epic ID like mentioned above):
The restrictions outlined above apply to V-bucks only. Any content purchased with your V-bucks will be available across platforms.