The special ability soothing voice is a neat but limited trick
The 1st-level half-elf bard racial substitution level replaces countersong with soothing voice (Races of Destiny 157), which is like the bardic song fascinate but different, so below I've inserted soothing voice's differences into the description of the typical bard's fascinate special ability:
A half-elf bard with 3 or more ranks in the Diplomacy skill can use his voice to cause one creature to be affected by a calm emotions effect. The creature to be affected must be within 30 feet, able to hear the bard, must be able to understand the language the bard is speaking, and able to pay attention to him. The bard must also be able to see the creature. The distraction of a nearby combat or other dangers prevents the ability from working. For every three levels a bard attains beyond 1st, he can target one additional creature with a single use of this ability.
To use the ability, a bard makes a Diplomacy check. His check result is the DC for the affected creature’s Will save against the effect. If a creature’s saving throw succeeds, the bard cannot attempt to fascinate that creature again for 24 hours. If its saving throw fails, the creature is affected as if by the spell calm emotions [Note: Several omitted sentences appear here that the DM could, potentially, apply also to the special ability soothing voice, but I have assumed here they are, instead, relevant to the special ability fascinate. Ask the DM.]
This effect is an enchantment (compulsion), mind-affecting ability.
While the spell calm emotions is usually is a 2nd-level spell (therefore usually not available until at least character level 3 and higher than that for a bard), its usual range is medium, its usual area is a 20-ft.-radius spread, and its usual duration is concentration (up to 1 round/level). Although the special ability soothing voice's save DC will be higher than the spell—based as it is on a Diplomacy skill check—, a low-level character being able to use a few times per day this special ability (that draws its uses from the same pool as inspire courage, by the way) isn't overpowered, especially considering that the bard must have languages sufficient to be able to make himself understood to the creature (unlike the song fascinate) and that affected creature can just walk away if the bard's uninteresting (which is insulting and hilarious).
At higher levels, soothing voice is probably a waste of the bard's time, with him having much better things to do with his bardic music ability and him having spells that will do what he was trying to do with soothing voice better than soothing voice, but soothing voice may yet even then give the bard the opportunity to use his real Diplomacy skill, a skill that can wreck the game in the wrong hands. That is, at least, until higher levels in which the vast majority of creatures are immune to mind-affecting effects (you know, like the special ability soothing voice).
Note that spell calm emotions neither erases memories nor changes attitudes. If Baracs strolls into the orc camp, murders the orc warlord, is caught red-handed by the warlord's lover, uses soothing voice on the warlord's lover, and the lover fails the saving throw, the lover will (greatsword in hand) calmly discuss with Baracs his actions and impending demise as he escorts Baracs to a cell. The warlord's lover, even while affected by the spell calm emotions, can still call for help, alerting the camp, and Baracs just won't have enough soothing voices for the whole tribe. And the minute Baracs tries something aggressive (and a DM may rule that a murderer caught red-handed who then tries to flee a crime scene is behaving aggressively), all bets are off, and swords start swinging.
The spell calm emotions gives the caster a brief respite in which to catch his breath and perform some minor, non-aggressive actions, most often the spell offering an opportunity to for the party to enter into an otherwise implausible parley. It does shut down melee attackers, but while the effect lasts it also essentially shuts down the party. (That is, "The distraction of a nearby combat or other dangers prevents the ability from working.") Unless the party's worked out tactics beforehand for ambushing becalmed monsters (which is at least rude if not outright evil), the only thing a calm emotions effect will really do is let the user talk to one or more creatures that were, moments before, trying to kill him.
I can imagine that might be overpowered in some campaigns, but I suspect those campaigns probably wouldn't allow such a special ability to be taken in the first place.
In general, bonuses of the same type do not stack. This means that all allies will only get the highest single morale bonus for the circumstance between Banner and Flagbearer. Since Banner of the Ancient Kings doubles the bonus from Flagbearer, the Banner bonuses only apply to allies outside the 30ft range of Flagbearer but that are within the 60ft range of Banner.
The results would be:
+4 total against fear and charm:
+2 morale from Flagbearer (+1 x2 from BotAK), +2 resistance from Banner of Ancient Kings
+2 against other mind-affecting: +2 resistance from Banner of Ancient Kings
+2 bonus on attack rolls: Flagbearer grants a +2 morale bonus on attack rolls (+1 x2 from BotAK)
+2 damage on attack rolls: Flagebearer bonus x2 (+1 x2 from BotAK)
+4 on initiative: +4 circumstance bonus on Banner of Ancient Kings
As long as you wield the spear in two hands, I don't see why the bonuses are gone as soon as you attack -- they should remain and apply to allies as long as they can see the banner. On the other hand, if you use a shortspear, you can still attack by wielding the weapon in two hands but you can't attach your banner of the ancient kings to it ("As long as the longspear or pole to which the banner is attached is wielded in two hands...").
Best Answer
It does not
Bard's Inspire Courage only works on weapons, meaning that anything that isn't considered a weapon will not get this bonus.
For instance, it will work on a magical ray spell, as those are considered weapons (see this FAQ). Or even weapon-like spells, such as Spiritual Weapon or Flame Blade. But it will not work to increase the damage of Magic Missiles or a Fireball, for instance.
This means that the swarm automatic damage wouldn't benefit just like a Fireball also wouldn't, as there is no attack roll involved, and there is no weapon in the ability's description. On the contrary, it is described that the Swarm attack replaces the normal attacks, and this attack is not described as a weapon attack at all. From the Swarm subtype:
On top of that, Inspire Courage is described as a Mind-affecting ability, which will rule out nearly all vermin-swarms right away. But mind-affecting effects that have no number of targets could affect a swarm, as they are only immune if the effect hits a specific number of targets:
This means that, even if the swarm wouldn't gain the bonus to weapon attacks and damage rolls, they could still benefit from the saving throw bonus against fear effects, if the conditions above are met.
Since nearly all published hive minds are also vermin or have no Intelligence score, or simply have immunity to mind-affecting effects, that also rules them out. There are two exceptions, though, the Bettle Swarm Hivemind (Occult Bestiary), and the Hivemind Swarm (Bestiary 6).
Regardless, none of them are actually described as able to make weapon attack/damage rolls, as such, there is nothing for Inspire Courage to enhance there.