Vivisectionist alchemist:
If you have vestigial arms discovery and are holding an akyl (exotic light melee weapon, 20 ft range) and also wielding two pistols (assuming someone melee is directly opposite), do you get sneak attack with your pistols by threatening with the akyl? Do you get sneak attacks with both guns?
No, ranged flanking isn't a thing. Not even with snapshot. Threatening with a melee weapon does not allow you to threaten with other weapons either.
The concept of 'ranged flanking' doesn't currently exist in Pathfinder. It does exist in D&D 4E, where you can take a feat to get 'combat advantage' bonuses at range.
There are really only a couple of options for getting sneak attack at range. A couple of examples: you can use the sniping rules, you can be invisible, or you can use the Dazzling Display and Shatter Defenses combo.