My question involves Exemplar and Banner of the Ancient Kings
Specifically the Exemplars:
At 3rd level, an exemplar gains the ability to use certain bardic performances. She can use this ability for a number of rounds per day equal to 3 + her Charisma modifier; this increases by 1 round per brawler level thereafter. The exemplar’s effective bard level for this ability is equal to her brawler level – 2. At 3rd level, the exemplar can use inspire courage. At 11th level, the exemplar can use inspire greatness. At 15th level, the exemplar can use inspire heroics. Instead of the Perform skill, she activates this ability with impressive flourishes and displays of martial talent (this uses visual components).
This ability otherwise functions as bardic performance; feats and other effects that affect bardic performance (such as the Extra Performance feat) apply to it.
and the latter part of the rules for Banner of the Ancient Kings
This tattered white canvas banner looks like an old piece of sailcloth, or perhaps a winding shroud—a 4-foot-by-6-foot rectangle with loops that can fit over a spear haft or pole running up one side. If mounted on a longspear or pole at least 8 feet in length, the banner shifts in appearance to match the heraldry or coat of arms of the person who attached it. If that person has no device, the flag instead displays a device that echoes the owner’s personality (such as a favorite animal, favored weapon, or holy symbol of the wielder’s deity).
When carried into battle, a banner of the ancient kings confers several benefits. As long as the longspear or pole to which the banner is attached is firmly wielded in two hands, its carrier gains a +4 circumstance bonus on Initiative checks. In addition, when so wielded, it grants the wielder and all allies within 30 feet a +2 resistance bonus on all saving throws against mind-affecting effects. If the carrier of the banner fails a saving throw against a mind-affecting effect, he may attempt a new saving throw against that effect every round he continues to wield the banner of the ancient kings—once he releases his firm grip on the banner’s haft, though, he no longer gets this benefit, even if he wields the banner properly at a later point while still under the effects of the mind-affecting effect.
If the banner’s carrier possesses the Flagbearer feat, the banner of the ancient kings doubles the morale bonuses granted by that feat. A bard who carries a longspear or pole to which a banner of the ancient kings has been attached is treated as four levels higher than his actual bard level for the purposes of determining the bonuses granted by his inspire courage bardic performance ability.
Does an Exemplar count as 4 levels higher when carrying the Banner?
I think this is actually the part the allows you to effectively use the Flagbearer/Banner of Ancient Kings combination:
"... The exemplar’s effective bard level for this ability is equal to her brawler level – 2..."
But, to answer your question, yes... everything should work as you expect it to.