Meaning: a wonderful, sentimental moment (sometimes meant satirically) (example 1, example 2)
Rewrite 1: a Kodachrome frame
Rewrite 2: a soft-focus moment
Rewrite 3: get all Kodacky on me
Rewrite 4: here's a picture shy on sincerity
Rewrite 5: a photo-op moment
Comment: The danger with this idiom is that with the demise of Kodak, the "Kodak moment" now may slip into obscurity or fall into a sense of the no-longer-relevant.
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