At second level a Storm Kindler can use the Whirlwind monster ability for a bit of time each day. Part of that ability is automatic unarmed strike damage against enemies that fail a save, like the normal whirlwind's Slam damage.
If the Storm Kindler has a Slam attack from some source or another, are they allowed to make this attack instead? Full text for the Storm Kindler ability and Whirlwind follow.
As a swift action, the Master of Storms can change the height of her whirlwind form from a minimum of 10 feet tall to a maximum of 20 feet tall.
At 4th level, and again every two levels thereafter, the maximum height of the whirlwind increases by 10 feet, to a maximum of 60 feet tall at 10th level. If the Master of Storms is underwater when she uses this ability, she instead transforms into a vortex of the same size (this functions identically to the whirlwind ability, but can form only underwater and can't leave the water). The Master of Storms can breathe water while in vortex form. If the Master of Storms does not possess a fly or swim speed, she gains one (as appropriate to her new form) equal to her base land speed when in storm shape. With a fly speed, she has average maneuverability.
The Master of Storms can damage and trap Small or smaller creatures caught in her whirlwind, dealing lethal damage equal to her unarmed strike damage to each one that fails a Reflex save (DC 10 + the Master of Storms's class level + the Master of Storms' Strength modifier) and lifting it into the air if it fails a second Reflex save.
At 4th level, and again every two levels thereafter, the size of creatures the Master of Storms can affect increases by one step, to a maximum of Huge at 8th level.
The whirlwind is always 5 feet wide at its base, but its height and width at the top vary from creature to creature (minimum 10 feet high). A whirlwind’s width at its peak is always equal to half of its height. The creature controls the exact height, but it must be at least 10 feet high.
The whirlwind form does not provoke attacks of opportunity, even if the creature enters the space another creature occupies. Another creature might be caught in the whirlwind if it touches or enters the whirlwind, or if the whirlwind moves into or through the creature’s space. A creature in whirlwind form cannot make its normal attacks and does not threaten the area around it.
Creatures one or more size categories smaller than the whirlwind might take damage when caught in the whirlwind (generally damage equal to the monster's slam attack for a creature of its size) and may be lifted into the air. An affected creature must succeed on a Reflex save (DC 10 + half monster’s HD + the monster’s Strength modifier) when it comes into contact with the whirlwind or take damage as if it were hit by the whirlwind creature's slam attack. It must also succeed on a second Reflex save or be picked up bodily and held suspended in the powerful winds, automatically taking the indicated damage each round. A creature that can fly is allowed a Reflex save each round to escape the whirlwind. The creature still takes damage but can leave if the save is successful.
Creatures trapped in the whirlwind cannot move except to go where the whirlwind carries them or to escape the whirlwind. Trapped creatures can otherwise act normally, but must succeed on a concentration check (DC 15 + spell level) to cast a spell. Creatures caught in the whirlwind take a –4 penalty to Dexterity and a –2 penalty on attack rolls. The whirlwind can have only as many creatures trapped inside at one time as will fit inside the whirlwind’s volume. The whirlwind can eject any carried creatures whenever it wishes as a free action, depositing them in its space.
If the whirlwind’s base touches the ground, it creates a swirling cloud of debris. This cloud is centered on the creature and has a diameter equal to half the whirlwind’s height. The cloud obscures all vision, including darkvision, beyond 5 feet. Creatures 5 feet away have concealment, while those farther away have total concealment. Those caught in the cloud of debris must succeed on a concentration check (DC 15 + spell level) to cast a spell.
Format: whirlwind (3/day, 10–30 ft. high, 1d6+6 damage, DC 15); Location: Special Attacks.
I really like the flavor of the class, but I'm still trying to figure out how to not be a burden to my table when playing one.
I don't think so. Whirlwind damage is "generally damage equal to the monster's slam attack for a creature its size", but it is not required to be. Since the Storm Shape ability specifies the intended damage, that damage is the amount dealt. On the bright side, if you have monk levels or other means of improving your unarmed strike, they improve your whirlwind.
It can go either way. You can argue that the specific rule for Storm Shape overrides the more general rule of Whirlwind, so you have to use the unarmed strike damage. Alternatively, you can see that caveat of the Storm Shape as simply a placeholder to handle the fact that most PCs do not have slam attacks, so here's a quick alternative solution.
I'd say the most 'correct' interpretation is the first one. It says unarmed, you get unarmed. However, in any game I were to run, I'd allow the second one.