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A Zen Archer Monk is perfectly self-sufficient in providing all the feats you'll ever want in Archery, so I wouldn't think Ranger or Fighter would be necessary.
Also, you Flurry as a Full BAB class, so that doesn't do much for you (CMB and CMD, standard attack actions... But eh.)
I would say you should go one of two routes: Cleric/Druid/Sorcerer or Inquisitor.
That's basically what it would come down to for me. Either go for full caster with very few class features boosting your archery, or go with the mediocre spellcasting with a bunch of class features that compliment you.
Let's see what an Inquisitor has to offer compared to a full caster.
+6 Skill Ranks per level and more Class Skills
Judgments to improve archery
Bane class feature to improve archery (Absolutely fantastic, by the way)
Stalwart class feature (Add in Ring of Evasion and that's all 3 saves!)
+Wisdom to Initiative
+Wisdom to Knowledge Checks
Wisdom instead of Charisma to Bluff, Diplomacy, and Intimidate (If taking the Conversion Inquisition)
Well, you can read the rest, but yeah. Inquisitor is tough to beat, it takes your archery up to a whole new level, makes you even more durable and you're going to almost always act first.
On the other hand, there's full casting. Which is absolutely fantastic and shouldn't be dismissed in the slightest. However, personal preference, if I had the opportunity to Gestalt, I would go for something with a lot of synergy rather than two aspects that are individually powerful.
ZAM is amazing. Full casters are amazing. Both on the same character? Well, better than either I guess, but you can't cast AND flurry on the same turn, so limited synergy.
ZAM is amazing. Inquisitor is good. Both on the same character? Absolutely fantastic. The Inquisitor really enhances everything you love about being a ZAM.