If i have an informed acolyte (any learned character) in play with a standing advisors chambers. Am i able to play princes plans (4 influence cost) by kneeling the advisors chambers, then kneeling the acolyte to stand the chambers and then kneel the chambers or is there no window for that to happen?

The answer lies in the fact that these are two separate player actions. The rules clearly state that a new player action cannot be initiated until the current action is resolved. So there is simply no opportunity to stand The Advisor's Chambers until you have fully paid the influence cost and resolved the effect of The Prince's Plans.

On a more conceptual scale, there is no "influence pool." Kneeling a card to produce influence is not an ability of the card, so you cannot "save" influence between triggering effects. For example, kneeling The Red Keep (3 influence) will not let you play 3 separate copies of The Prince's Wrath. You effectively waste the 2 influence you over pay. The situation here is the same thing, from the opposite direction (as J-Roel explained).