[RPG] Can you teleport or Dimension Door out of your clothes

Shadow Cloak

Activation: — and immediate (command)

The information above is pulled directly from the items info. We see that it takes an immediate action to activate either of its command effects.

For reference,

Swift Action A swift action consumes a very small amount of time, but represents a larger expenditure of effort and energy than a free action. You can perform only a single swift action per turn.

Immediate Action An immediate action is very similar to a swift action, but can be performed at any time — even if it's not your turn.

The information on the Cloak states

If you are attacked, you can use the cloak three times per day to produce one or the other of the following effects. You can gain concealment for 1 round, or you can teleport to a space you can see clearly up to 10 feet in any direction.

So it only works against an action defined as an attack. As such you need to decide what exactly a grapple is considered to be.

http://www.d20srd.org/srd/combat/actionsInCombat.htm

Has Grapples listed under its miscellaneous actions Table near the bottom of the page.

The note connected to it says

2. These attack forms substitute for a melee attack, not an action. As melee attacks, they can be used once in an attack or charge action, one or more times in a full attack action, or even as an attack of opportunity.

So Grapples according to the SRD are defined as Melee Attack Actions. As such...

The Shadow Cloak would allow you to escape from a grapple attempt. It cannot however be used to escape from within an already successfully established Grapple.

The spell dimension door allows the caster to travel instantaneously "from [the caster's] current location to any other spot within range. [Casters] always arrive at exactly the spot desired—whether by simply visualizing the area or by stating direction." Up—to the limit of the spell's range and the caster's desires—is certainly possible (albeit risky if the destination hasn't been scouted first).

The spells teleport et al. can do the same, although there's a chance of mishap with some effects and the caster "must have some clear idea of the location and layout of the destination." Achieving knowledge of up by looking skyward is totally legit.

However, it's really complicated to employ an instantaneous travel effect like those above so that the benefit of the feat Death from Above can be realized as that feat's benefit requires the creature to "charge an opponent from higher ground… [to] gain a +5 bonus on attack rolls in place of the bonuses from charging and being on higher ground."

That is, while making the charge the creature must take a free or swift action to activate the instantaneous travel effect then the GM must rule that the creature did not violate the stiff restrictions on making a charge in the first place: a charging creature "must move to the closest space from which [it] can attack the opponent." Since taking a full-round action to charge is nearly unique among actions in that it requires a declaration of intent before the action's actually taken, a GM may rule that the space is picked when the charge is declared and that the creature's charge is foiled by its own mid-charge instantaneous travel effect, probably because the creature ends up attacking from a different space than one the creature would've been attacking from when the charge was declared. Ask the GM.

However, keep in mind that unless the creature can also fly, after the creature's instantaneously traveled upward, the creature will fall and—unless the surface is more than 500 ft. below the creature—, also, land. Like, right now! There's no chance in such cases, for example, for the charger-now-caster-now-charger-again to attack the foe from higher ground before falling, cartoon physics to the contrary.