Would consume magic item or consume spell affect a magic rune on a chest?
I reread Consume spell this looks like it would work as the arcanist would make a dispel check againist the rune.
Am I right?
Absolutely not. The ability very clearly states "The arcanist can consume the power of potions, scrolls, staves, and wands, using them to fill her arcane reservoir." That rune is not one of the above mentioned items. Even if you have an item that works similar to one of the above (like an Elixer) it won't work because its not one of the 4 kinds of magic items the ability works on.