I believe the percentage goes on first, then the flat damage blocks, and lastly any damage caps. I will list a couple examples for this.
Agent Coyle, Immovable in defense with Wall of Jinhai in play, and a Zunshen having been played that turn gets attacked by a One of Many and a Skraar. Skraar (being in the lead) hits for 15, but that is halved (and I believe rounded down) to 7. It is then dropped by 2 due to the wall to a 5. Lastly, Agent Coyle can take no more than 3 damage so it gets capped at 3. One of many does 8 damage which gets halved to 4, then dropped to 2. It is less than the cap of 3, so Agent Coyle takes a total of 5 damage from the two attacks. I've tested this in the past, but I forget the exact order. It's either the flat damage blocks 1st, or the halving 1st, but the chance of it hitting for only 1 I can assure you will not happen. If I get the chance to try this again, I'll update my post here, unless someone has confirmed before I try it.
EDIT: Confirmed. Damage is halved before it is reduced by flat damage. There you go.