Bu RAW, the interact surprising well.
Being Aid Another a specific action, whose normal timing is a standard action, the feat and class feature you cited merely modify different aspects of it.
Aid Another has a positioning requirement (you must be able to perform a melee attack vs. a target) and lets you take a standard action to make an attack roll against the target (vs. AC 10). If you hit you either give an ally a +2 untyped bonus to AC (against target's next attack) or a +2 untyped bonus to the first attack roll (against the target). Its duration is up to the beginning of your next turn.
Swift Aid lets you perform and Aid Another action as a swift action. The verb granting in
"Benefit: As a swift action, you can attempt the aid another action, granting your ally either a +1 bonus on his next attack roll or a +1 bonus to his AC."
seems to point out that the +1 bonus replaces the normal +2 bonus.
Aid Allies, as written, grants an additional and untyped bonus to a quality of your choice (AC, attack roll, saving throw, or skill check). It is not clear which saving throw and skill. This is a rider effect on top of what aid another normally allows. Meaning you could choose to aid another granting him a +2 bonus to the next attack roll against the target, and a +3 bonus to his AC; or granting him a +2 bonus to the next attack roll against the target and an additional +3 bonus on all attacks. Not clear what the duration of the Aid Allies feature is (supposedly to the beginning of your next round).
So, the feat and the class feature should interact this way.
You can use aid another as a swift action. If you choose this way, your ally receives only a +1 bonus either to AC vs. the target's first attack, or to the first attack roll he performs against the target. Furthermore, because you used the aid another action, he receives a +3 (stackable) bonus to a quality of your choice (AC, attack roll, saving throw, or skill check).
However, rules as written probably differs from rules as intended. And this opinion comes from the poor wording choice the designers used. Swift Aid hints to a replacement effect, but do not clearly states so. Aid Allies lacks information outright:
- Is it a replacement effect?
- If no (that is: is a rider effect), which is its duration?
- If yes, what exactly replaces?
- Is the attack roll bonus only granted for the first attack? Is it granted only against the target?
- Is the AC bonus bonus only granted for the first attack? Is it granted only for attacks coming from the target?
- Which saving throw is affected? Is it granted only for attacks coming from the target? Only once or even multiple times in a round?
- Which skill check is affected? Must it be something related to the target? Only once?
Under the hypothesis it is considered a replacement effect, and focusing only on AC and attack rolls, I'd say that you cannot use two replacement effects simultaneously. So, you either use Aid Allies as standard action (granting a +3 bonus) or use Swift Aid as a swift action (granting a +1 bonus).