If a magic item, such as the iron flask (Wis save; DC 17) or Mace of Disruption (Wis save; DC 15), has a DC save that a target or afflicted individual must succeed on, is there any way to influence this number to lower or raise the DC of the item and its property effects?
It's hard to prove a negative, but as far as I can tell, there's no RAW way to modify a magic item's DC.
There does seem to be a rough correlation with the rarity of the magic item and the save DC, which makes a lot of sense: an Eyes of Charming that's DC 20 is a lot more powerful than the standard DC 13. Thus, tweaking the save DC of a magic item would probably be enough to change its rarity category, sometimes significantly. In-universe, this fixed DC makes sense because it's an inherent quality of the magic item, rather than its user.
Unfortunately, there are no guidelines for setting what the save DC should be at each rarity level. It seems to vary significantly within the same rarity, and the section in the DMG about custom items does not address save DCs.