This Should Work
Since Dual Thrower works with the strikes form Double Slice as it allows you to substitute in a ranged weapon strike for a melee weapon strike for any feat that is obtained as part of the Dual-Weapon Warrior archetype.
So, Double Slice and Dual Thrower: check.
Now, looking at Flensing Slice, we see that the Requirement for it is simply “Your last action was a Double Slice, and both attacks hit the target.” It doesn’t specify that the attacks had to be melee, just that they had to hit. After meeting that requirement, the meat of the feat states:
The target takes 1d8 persistent bleed damage per weapon damage die of
whichever of the weapons you used that has the most weapon damage dice
(maximum 4d8 for a major striking weapon). The target becomes
flat-footed, and its resistances to any physical damage types are
reduced by 5; these two effects last until the beginning of your next
Again, no requirement for melee weapons. So the chain is just so: You use Double Slice. Dual Thrower allows you to substitute your bombs for those attacks. Both of those attacks hit, and since your last action was Double Slice and they both hit, you can use Flensing Slice.
Yes, considering the imagery of flensing with a bladed weapon, it seems odd to somehow do that with a thrown one, but flensing is simply stripping off skin (or blubber), which a good explosion or acid bath can do. Don’t let the “Slice” part of Flensing Slice throw you either – the names often take artistic license, and are not meant to restrict (or add to) the actual crunch. For example, the spell Grease gets a lot of attention because some people insist that the resulting grease should be flammable because grease often is. But, similar to D&D 5e, things do what they say they do – no more, no less. So flensing strike does damage, imposes flat-footed, and reduces physical resistance. That’s it. It doesn’t necessarily flense or slice – all of that is just fluff, and thus easily changeable without affecting balabnce.