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Ran part of a module (Ruby Phoenix, so perhaps a mild spoiler here) recently, and couldn’t find a definitive answer at the time, so I went with what I thought was a logical answer, and wanted to see if there was a more definitive answer somewhere.
The situation involved an oracle with a ring of blinking and the wall of fire spell (though there are plenty of other types of secondary concealment that could fit in the example - fog cloud, invisibility, deeper darkness, etc.) Once the caster activates the ring, they have a 20% miss chance on their own physical attacks, and a 50% miss chance for physical attacks made against them, by virtue of the fact that they’re bouncing back and forth between the material and ethereal planes (a timing question, but also partly visual, since the spell stipulates that your enemies’ miss chance goes down to 20% if they can see invisible creatures, but they get no benefit if they have the Blind Fight feat, and also points out that ethereal creatures are both invisible and incorporeal):
http://paizo.com/pathfinderRPG/prd/coreRulebook/spells/blink.html
Kinda fiddly, but all pretty workable. What happens however when a subject under blink adds a second effect with a miss chance to the effect? In this case the caster had two high level barbarians bearing down on her, so she surrounded herself with a small-radius wall of fire, pointing it outwards. The wall of fire provides total concealment, blocking line of sight, by virtue of being “opaque.” Ordinarily, attacking a foe on the other side of such a wall would be a 50% miss chance, though stuff like the Blind Fight feat or some creatures’ ability to see through flames would reduce or negate the miss chance.
http://paizo.com/pathfinderRPG/prd/coreRulebook/spells/wallOfFire.html#wall -of-fire
So, with both of those effects in play, what are the miss chances for the blinking oracle on one side of the wall, and the raging barbarians on the other side (no one involved had Blind Fighting or the ability to see through flames.
The simplest “go away and stop making us think hard” answer is just a flat 50% for everyone based on the wall of fire, using the idea that miss chances shouldn’t stack.
The harshest position is to say that since they’re from fundamentally different sources, resolve them separately, meaning the barbarians have to get through a pair of 50% miss chances, while the oracle has to get past a 50% miss chance and a 20% miss chance. This is what I went with under the time crunch and not wanting to bring the game to a screeching halt. Alternatively, you could resolve the percentages into a single roll and say the barbarians have a 75% miss chance (50% + 50% * 50%) and the oracle has a 60% miss chance (50% + 50% * 20%).
An in-between position would be to say that since the wall of fire renders other visual considerations moot, but the 20% portion of blink’s miss chance would still apply, then the barbarians should be contending with a 50% miss chance and a 20% miss chance (aggregate of 60%). Still another interpretation would be that see invisibility reduces blink’s miss chance because you can see the subject on both planes, but the Blind Fight feat doesn’t help because... you pick the mental and physiological reason that makes sense to you, so the 75% total should be reduced, but only to some other value between 75% and 60%.
In the event that no definitive answer to this already exists, happy debating! :)
I'd go with the second option, roll once for the wall of fire miss chance due to concealment, roll again for the blinking miss chance for being out of phase.
Blink is weird.
What happens if an invisible creature steps into dim light? Does it get a 50% miss chance and a 20% miss chance? No, it gets a 50% miss chance because dim light is irrelevant when you're already invisible. More to the point, 50% miss chance is pretty much the maximum you can get--it even applies when attacked by a blind creature. The same argument works for an invisible creature in a fog cloud or an invisible creature being attacked by a blind creature.
But then there's blink, which applies a miss chance from literally not being there to hit some of the time. I can see the argument that they should be run sequentially in that case since they're independent effects and neither affects the relevance of the other. After all, not all concealment is the same--darkvision overcomes concealment from dim light but not fog, while fogcutting lenses does the opposite. It's reasonable to rule differently based on the specific mechanisms of concelment.
All in all, I'd roll blink separately.
I'd roll blink separately at the 20% change of not being there, because the "visibility" portion of the spell is irrelevant.
Blink (20%) = Ethereal
Blink (50%) = Invisible
Wall of Fire (50%) = Opaque sheet of flame granting Total Concealment
Let's say the same conditions. A creature has an active Blink effect and surrounds themselves in a Wall of Fire.
Scenario 1:
Creature's can't see through the Wall of Fire. The fact that Blink makes her invisible is meaningless, so she doesn't benefit from that concealment.
On the attack roll, roll the miss chance for total concealment. If they miss, they would not have hit her no matter what her Blink status was. If they make the Total Concealment from the Wall of Fire, then roll the 20% miss chance granted for potentially being Ethereal. (Or you can combine this to an equally likely 60% miss chance. However, if your players are unfamiliar with probability, I suggest making two separate rolls. It may also make them "feel better" about their spells working / not working.)
Scenario 2:
The creatures have an ability to see through fire.
You can see through fire, fog, and smoke without penalty as long as the light is sufficient to allow you to see normally. At 7th level, you can gaze through any source of flame within 10 feet per oracle level, as if using clairvoyance. You can use this ability for a number of rounds per day equal to your oracle level, but these rounds do not need to be consecutive.
The attackers now can see through the fire. Blink grants its 50% miss chance.
Scenario 3:
The creatures have an ability to see through fire AND invisibility.
Blink grants its 20% miss chance.
Blink has two overlapping effects:
1) I am ethereal part of the time
2) I am invisible part of the time
If both affect you, 50% miss chance.
If only one affects you, 20% miss chance.
If neither affect you, 0% miss chance.
The Wall of Fire gives 50% miss chance.
Miss chance for a given reason does not stack. So you get the 50% from 'cannot see' and the 20% from 'not here'. They would be processed separately.
You could add in Wind Wall for another source of miss chance that stacks since it is a 'something is blocking' type of miss.
/cevah