Armor does usually count toward a creature's maximum load
The 3rd-level Sor/Wiz spell fly [trans] (Player's Handbook 232) offers a very specific case wherein the above is not true, but the general rules typically apply to all other creatures. So, yes, to determine the creature's load "total the weight of all the [creature's] items, including armor, weapons, and gear" (161 and emphasis mine).
To be clear, the exception offered by the fly spell is as follows:
The subject can fly at a speed of 60 feet (or 40 feet if it wears medium or heavy armor, or if it carries a medium or heavy load).… The subject of a fly spell can charge but not run, and it cannot carry aloft more weight than its maximum load, plus any armor it wears. (232)
This is complicated but not contradictory. For example, Gniylfmi, a human wizard, possesses Str 7 and casts on herself a fly spell.
- If she's only wearing studded leather (PH 123, 126) (25 gp; 20 lbs.), her fly speed's 60 ft. due to light armor and a light load.
- If she's only wearing a chain shirt (123, 124) (100 gp; 25 lbs.), her fly speed's 40 ft. because of the medium load caused by wearing the light armor.
- If she's only wearing chainmail (ibid.) (150 gp; 40 lbs.), her fly speed's 40 ft. because this is both a medium load and medium armor.
- If she's carrying 70 lbs. of gear and wearing full plate (ibid.) (1,500 gp; 50 lbs.), her fly speed's 40 ft. because the spell lets her ignore the armor's weight when she's carrying her maximum load. However, were she to attempt to use her land speed, "she can only stagger around…, loses any Dexterity bonus to AC[,] and can move only 5 feet per round (as a full-round action)" (162) because this is more than her heavy load but less than over twice it.
This could put Gniylfmi in the unusual position of saying, "Yeah, I'll carry it. I'll already be at a heavy load and I've a few more pounds I can carry because of my armor." That is a little bit more bookkeeping, but in a game that already requires acres of bookkeeping I'm not sure the impact is that great.
Note: Neither Player's Handbook errata (Feb. 2006) nor the premium edition Player's Handbook (2012) that includes stealth errata touches the fly spell.