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When/How would the Android Flat Affect racial trait apply if an Android is attempting to use the bluff skill to lie?
Flat Affect:
Androids find emotions confusing and keep them bottled up. They take a –2 penalty to Sense Motive checks, but the DCs of Sense Motive checks attempted against them increase by 2.
Bluff(Lie):
...If the creature is suspicious or attending carefully to your lie (as per the detect deception task for Sense Motive), the check is opposed by the Sense Motive check of the creature you are lying to; otherwise, the DC of this check is equal to 10 + the creature’s total Sense Motive skill bonus.
Sense Motive(Detect Deception):
...Your Sense Motive check is opposed by that creature’s Bluff check.
According to the wording of both skills, the other is the opposition skill in an opposed check, so which one sets the DC of the other? Flat Affect only increases the DC to Sense Motive checks against the Android and does not apply a penalty. Would this mean that a suspicious listener has a harder time detecting an Android's falsehood?
If the determination on which skill sets the DC is that it is always the NPC roll, then this racial trait is a universal penalty to Androids players with no benefit. Meanwhile, all NPC Androids would be especially convincing liars.
I would say in this case the Android does get a +2 to his bluff, effectively. I think in this case the Bluff role sets the DC of the Sense Motive check, hence a +2.
So what happens on a tie?
My guess is the sense motive roll wins (in the same way meeting a DC succeeds.) Hence, bluffer sets the DC.
Neither one "sets" the DC for the check; instead, the two checks are opposed, meaning they each roll skill checks normally, and the one with the higher result succeeds.
Basically, androids get a +2 to their bluff attempts, and get a -2 to their attempts to detect other people's bluffs.
@quasiconundrum
The rules, as written, say the exact opposite of what you stated:
"Sometimes you attempt a skill check not to accomplish a task, but to thwart someone else’s task or action. This is called an opposed skill check. With an opposed skill check, one creature attempts a skill check to try accomplish some action or task, while another creature attempts its own skill check to determine the DC the first creature must meet or exceed to accomplish its goal."