Hi,
I am afraid you are not being clear.
What is asking for the AIM password ?
Is it the iMessages Account ?
Or are you using an Apple Issued ID as an AIM valid Screen Name ?
@mac.com @me.com ID linked to iCloud and @icloud.com IDs can be used and AIM valid Screen Names and would use the same Apple ID password
However if you have 2 Step Verification on the Apple you may not need it is you are using it as an AIM valid Screen Name as there is a double check already with the app logging into AIM and Apple to confirm the ID.
If on the other hand you are using an AIM.com ID as your Apple ID then it will be the Password like to the ID at Apple.
If you are then using 2 Step Verification then Messages needs a App Specific one set up.

9:11 pm Monday; March 28, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad