If this is for PFS: None of the Oracle classes stack with each other. They all replace or change Class Skills and/or Class Spells received from their mystery. If the player wants to play "Healbot", then Life Oracle with the Pei Zin Practitioner is the best way to go (without Multiclassing Paladin). Duel-Cursed is good for any Mystery which you want to receive lots of revelations from and Fortune/Misfortune are both good Revelations themselves. Ancient Loorkeeper is good if they want to be a Spellslinger, as they get a Wizard/Sorcery spell added to their knowledge at every Even level and they are a spontaneous caster class.
If possible, sit down with your player and ask them specifically what they want to focus on as an Oracle. Unfortunately, with Archetype stacking rules, none of these Archetypes stack with each other.
If this is a Homegame: Do what you feel most comfortable with playing as the DM. If you're asking for advice on how to home rule this, I would suggest the following:
(1) "Duel-Cursed Oracles gain no additional class skills from her Mystery." - I would rule that this replaces both Pei Zin Practitioner's Master Herbalism and Ancient Lorekeeper's Class Skills. I.e.: They do NOT gain 1/2 Level on Profession (Herbalism) and do NOT gain Knowledge (Arcane) or Knowledge (Local).
(2) "Elven Arcana replaces all Mystery Spells" - I would rule that the Ancient Lorekeeper's Elven Arcana ability replaces all instances of Mystery Spells. This means that they do not gain ill omen (2nd), oracle’s burden (4th), or bestow curse (6th) from the Duel-Cursed Archetype. Pei Zin Practitioner is unaffected by this.
(3) "Level 1 and Level 7 Revelations are Still Locked" - Because Pei Zin Practitioner traits their Revolations at level 1 and level 7, they do not get to choose Duel-Cursed Revelations until their next available Revelation. I.e.: They can't take Misfortune level 1.
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TLDR - They don't stack by RAW, but if you're Homebrewing the game, nothing is preventing you from bending a few rules. Just make sure you're not giving /too/ much to this player. If you are playing PFS, then the answer is "No" unfortunately.
Hope that helps.