It's the latter. The rules for the kinetic blade form infusion are a more specific subject than those for all kinetic blasts, and specific rules trump general ones. You can use a kinetic blade/whip in a full attack and so attack multiple times with it according to BAB, haste and (whip only) attacks of opportunity.
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For clarity, lets parse the RAW, omitting the sections that don't deal with the question at hand (iterative attacks).
You can use this form infusion once as part of ... a full-attack action in order to make melee attacks with your kinetic blade.
The Kinetic Blade is not a standard action, it is part of your full-round action used to make melee attacks (plural).
Since it’s part of another action (and isn’t an action itself), using this wild talent doesn’t provoke any additional attacks of opportunity.
Further clarification: use of Kinetic Blade is not an action.
The kinetic blade deals your kinetic blast damage on each hit ... The blade disappears at the end of your turn.
Kinetic blast damage is applied on each (plural) hit until the end of your turn.
The kinetic blade is created as part of a full-attack action and applies to all attacks made by the character until the end of his turn. This can include AoOs made during the character's turn, e.g. an AoO provoked by Greater Trip.
The "specific" on abilities like this are usually pretty subtle. They tend to use terms such as "when" and "as".