Outflank: Your ally gets an AoO when you perform a crit while flanking.
Paired Opportunist: If an enemy provokes an ally, it also provokes from you.
Let's start with both you and your ally having the feats (and ignore fighter tactics for the moment).
You crit. This allows your ally to AoO, which from paired opportunist also allows you an AoO. The AoO you take crits, which triggers the set of AoOs from you and your ally again. Repeat till out of AoOs based on combat reflexes. Note that if your ally crits on any of their AoOs this will also trigger further AoOs.
This also works for a full attack action, where your BAB attacks all crit, generating AoOs for both you and your ally.
But now lets look at the case of your ally does not have the feats, but you have fighter tactics (or inquisitor solo tactics ability).
You are flanking and make a crit on your attack. Your ally does not have outflank though, so no AoO is generated for them. Because no AoO is generated for them, no AoO is generated for you from paired opportunist.
If your flanking ally however attacks and lands a crit, this generates an outflank AoO from you.
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All of the fighter’s allies are treated as if they had the same teamwork feats as the fighter for the purpose of determining whether the fighter receives a bonus from his teamwork feats. His allies do not receive any bonuses from these feats unless they actually have the feats themselves. The allies’ positioning and actions must still meet the prerequisites listed in the teamwork feat for the fighter to receive the listed bonus.
Only you receive any benefits from the feats. Your allies do not receive any benefits unless they also have the feats.
Benefit: Whenever you and an ally who also has this feat are flanking the same creature, your flanking bonus on attack rolls increases to +4. In addition, whenever you score a critical hit against the flanked creature, it provokes an attack of opportunity from your ally.
If you are flanking a creature:
1. Your flank bonus on attack rolls increases to +4. Your ally does not get an increase.2. When your flanking ally scores a critical hit you get an attack of opportunity. When you score a critical hit, nothing additional happens. Your ally doesn't get an AoO.
Benefit: Whenever you are adjacent to an ally who also has this feat, you receive a +4 circumstance bonus on attacks of opportunity against creatures that you both threaten. Enemies that provoke attacks of opportunity from your ally also provoke attacks of opportunity from you so long as you threaten them (even if the situation or an ability would normally deny you the attack of opportunity). This does not allow you to take more than one attack of opportunity against a creature for a given action.
1. When adjacent to an ally, you get a +4 bonus on attacks of opportunity. Your ally does not get a bonus.
2. When the enemy provokes an attack from your adjacent ally, it also provokes from you even if it normally wouldn't. Your ally does not get any additional benefit.If you score a critical hit, nothing happens. Your ally doesn't get an AoO, so neither do you.
Note that even if you both have both Teamwork feats, this combo doesn't work. You have to be both adjacent to your ally and flanking the enemy with the same ally to trigger all the effects. Which is impossible without additional feats that change flanking positioning requirements. Like Pack Flanking with an animal companion or Improved Outflank in very specific positioning.
Now, if you had something like a Cavalier's Tactician ability which allows you to share your teamwork feats with your allies then it can simplify things because now your allies do have the feats (while you're sharing them).
Fighter's Tactics basically works the same way as the Inquisitor's solo Tactics, which is to say that you can benefit from Teamwork feats as though your allies had them when they do stuff. Honestly they should have just said this works like Inquisitor's solo tactics.
@Belafon, I'm not so certain the second sentence of Paired Opportunist continues with the same qualifier of "when you are adjacent to your ally. Consider two rogues with the opportunist feat, the both namesake and most benefited example: the rogues want to be flanking excluding them from being adjacent, their opportunist attack now triggers for each other, and if they crit they get yet another attack of opportunity.
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@Belafon, I'm not so certain the second sentence of Paired Opportunist continues with the same qualifier of "when you are adjacent to your ally. Consider two rogues with the opportunist feat, the both namesake and most benefited example: the rogues want to be flanking excluding them from being adjacent, their opportunist attack now triggers for each other, and if they crit they get yet another attack of opportunity.
Also, Gang Up permits simultaneous adjacency and flanking.
Gang Up (Combat)
You are adept at using greater numbers against foes.Prerequisites: Int 13, Combat Expertise.
Benefit: You are considered to be flanking an opponent if at least two of your allies are threatening that opponent, regardless of your actual positioning.
Normal: You must be positioned opposite an ally to flank an opponent.
@Belafon, I'm not so certain the second sentence of Paired Opportunist continues with the same qualifier of "when you are adjacent to your ally. Consider two rogues with the opportunist feat, the both namesake and most benefited example: the rogues want to be flanking excluding them from being adjacent, their opportunist attack now triggers for each other, and if they crit they get yet another attack of opportunity.Also, Gang Up permits simultaneous adjacency and flanking.
Gang Up (Combat)
You are adept at using greater numbers against foes.Prerequisites: Int 13, Combat Expertise.
Benefit: You are considered to be flanking an opponent if at least two of your allies are threatening that opponent, regardless of your actual positioning.
Normal: You must be positioned opposite an ally to flank an opponent.
Assuming there is a third ally who is providing the flank to the one without gang-up yes, but that's an extremely niche case.