The archetype is broken.
They can't accept burn. They can't use any talent without gather power (ignoring other types of burn reduction). This essentially breaks the whole class because you're gimped in using infusions and you can never use defense talents and utility talents that require accepting burn (gather power only works on infusions). This is why overwhelming soul is one of the worst archetypes for the kineticist. Being able to use multiple blast types is strong, but not good enough to make most of the class's abilities useless.
Two abilities replace burn (which is impossible).
Most of the new abilities don't indicate what level you gain them. Archetypes should almost always indicate what level you gain an ability.
Wild Talents doesn't specify what type of wild talents have stunted progression. There are four types of wild talents, and the class receives them at different levels.
On top of it, I think there's already a 3pp archetype that does the multi-element thing.
One ability replaces burn. Accepting burn is not the same as using burn. (edit:derp) Which is why they are listed differently, however I fullyagree the wording on this needs work as the confusion will be common with new players.
As to wild talents: There is one type, wild talents. Elemental defenses are their own class ability as is infusions both of which are gained in their own time, so I do not understand your confusion on that point.
Elemental form is key to this archetype as it grants free use of the burn mechanic (to the point limit) each round while in use. This does mean utility powers can only be used while transformed but that's the idea. I do need to put in the standard increment use language.
Typically when an archetype replaces an ability it does so at the same level, but I can definitely clarify that and it would be a good addition
Edits: Ensured levels are stated for abilities.
Fixed the double tap on burn (you were right Cyrad) moved and adjusted wordingto better explain the adjusted burn mechanic.
No. There are four types of wild talents: kinetic blast, infusion, defense, and utility talents. All wild talents are listed by their type under the Wild Talent section of the kineticist class description. The class features call them wild talents. You say elemental defense is not a wild talent, but that class feature explicitly says "At 2nd level, a kineticist gains her element's defense wild talent." This is crucial because the class gets different types of talents at different levels, and some abilities only work on certain types of talents. This archetype is unplayable because it doesn't specify what wild talents have reduced progression.
Elemental form isn't that interesting to me. It still feels pretty bad because it means your class features are gimped for most of the day. A lot of utility talents aren't useful in combat. It also raises serious mechanical questions, such as what to do about wild talents with effects that last until you remove burn.
A new class feature should almost always specify what level a character gets it. This is a standard in archetype design. A player can't always assume it's the same level because many archetypes switch up the levels or have abilities that replace multiple class features (which is the case for your archetype).
Second round of edits: adjusted to clarify utility talents, added language to allow breaking up the duration on elemental form. Add language to clarify when talents end if they normally last until burn is removed.
Elemental form is how the archetype is supposed to be using utility powers. In the form he basically has 10 (20/30) points of burn he can spend per level, but he can't use them all at once.
That is something I do want to maintain, while realizing that it is an incredibly power effect over time.
Self recognized flaw:. Expanded elements needs to be addressed. Possibly simply all composite blasts to be available as level conditions and other prerequisites are met.
Edit: adjusted expanded element. Largely leaving the mechanic intact should be functional, and I am simply restricting it to the four elements the Suli have a tie to.