After every fill unless the filling mechanism does not lend itself to easy flushing. Even if I am using the same ink (does not happen often). For the few of those I have that are hard to flush, I try to use a dedicated ink for them. Really, I do not use pens like that very often. Now, if you mean CLEAN the pen, it depends on what I'm doing. I can't recall the last time I have cleaned a vintage pen after first assembly. Flushing is fine and the pen does not need it usually. And vintage pens have a potential to break.
That being said, I have a pen that has had Diamine Registrar's ink in it for over a year (yes, flushed every time before filled) and I am noticing it is starting to clog. I think some of the iron gall is beginning to build up a sediment. I read on another post recently I should do an Ascorbic Acid flush. I was going to attempt that and see if it helps before I do a full disassembly. It is an old vintage safety pen with a glass nib on it. I am not keen on disassembling it if I do not have to.
Ascorbic acid, now that's a new one! Do you maybe have a link to that post? And please tell us how it went if you do end up doing it!