In TF2, how do resistances against dual-damage-type weapons work?

For weapons such as the flare gun and the Detonator (which both have a dual damage type: namely fire and bullet), how is the damage dealt by these weapons affected by bullet and fire resistance?
e.g. What would be the overall effect of a flare gun hitting a Sniper wielding the Darwin's Danger Shield (15% bullet resistance) and the Bushwacka (20% fire vulnerability)? Would they simply stack additively, meaning that the flare gun would do +5% more damage to this Sniper?
Moreover, is the damage type split evenly? e.g. would an Engineer wielding the Southern Hospitality (20% fire vulnerability) experience 10% (half of 20%, assuming half of the flare gun's damage is fire-based and the other half bullet-based) more damage from the flare gun, or would it just receive 20% more damage?
I've tried looking on the damage page on the TF2 wiki, but I can't seem to find any information about dual damage types, and whether they stack.
If I'm not articulating myself properly, or am missing any details, please let me know.
Also, for the sake of simplicity, please ignore afterburn; I only care about the initial hit on the enemy.
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How does damage vulnerability work in tf2?
While under the effects, immune to all damage. +25% explosive damage vulnerability on wearer. When used, it provides a defensive buff to nearby teammates that blocks 35% of incoming damage, 50% of Sentry Gun damage, and nullifies Critical hits.Does Pyro have fire resistance?
So no, Pyro does not have any resistance beyond immunity to afterburn if you take him with base stats. Some gear provide reduction of damage to certain elements, such as fire and explosives, so that can affect your overall damage output as well.How much damage does afterburn do in tf2?
Afterburn damages a player every half-second for 4 HP each tick (1 HP each tick for the Degreaser), totaling 80 damage over those ten seconds (20 damage for the Degreaser).How much damage does the Scorch Shot do?
The Scorch Shot is a secondary weapon for the Pyro. It is a flare gun with a gray barrel and an orange painted muzzle, notably seen in Meet the Pyro. This weapon fires a projectile that can be reflected, but has a 50% damage penalty, so it deals 15 damage.TF2: How Damage Resistances Work
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