I'm no Kant expert, and I'm not a fan, but per my memory of this, Kant's negative/infinite distinction is about a contingent/necessary or accidental/analytic distinction, normally re classes.

In other words, it's about some set of Fs and whether we can predicate Gness of Fs.

A "negative judgment" here refers to a contingent or accidental fact that no Fs happen to be Gs.
An "infinite judgment" here refers to a necessary or analytic fact that no Fs are Gs.

We could extend that to particulars if we think of a particular as either contingently or necessarily having some property. So (1)--the flower necessarily isn't blue, or (2) the flower contingently isn't blue.

I don't recall the "provides knowledge" part so well, but if that's right, it would probably be based on something like "knowledge" providing information that's universally applicable rather than just a contingent fact.