The phrase "a kernel of a" is correct and usable in written English.
It can be used when referring to a small, essential part of a larger idea or concept.
Example: "There is a kernel of truth in every rumor, even if it is exaggerated."
Alternatives: "a nugget of" or "a grain of".
There's a kernel of a thrillerlike story tucked alongside the flabby love triangle formed by Anna, Dan and Zaid.
While playing up Trump's naivete is currently one strain of his political defense, legal analysts said it could also be a kernel of a criminal defense.
"Maybe at the end they'll have a kernel of a great idea," Mr. Battle said, but that is not a requirement of the program.
Here in her writing room, she sits in her ladder-backed chair, in front of her microphone, and takes a kernel of a melody or lyric and goes to work.
In October of 1991, Linus Torvalds, a 21-year-old computer-science student at the University of Helsinki, made available on the Internet a kernel of a computer operating system he had written.
Within its idealistic nature-rhapsody there's a sublimated love story as well as a kernel of a Bildungsroman, as, in the squire's words: Travellers flock hither from all quarters, and when the conversation turns on some town, or on some peculiar part of the globe, your guests are asked if they have never seen the same.
Sometimes it's the whole thing, sometimes it's just a kernel of an idea that you want to use.
The experience gave him a kernel of an idea for the reality television programs he later created.
Each year, he offers millions of dollars to young students, who often have just a kernel of an idea.
Narayan had a kernel of an entrepreneurial idea for a business she thought would make her life — and the lives of other parents — more manageable.
It quickly becomes very tiresome, which is a shame because for every three scenes of rote tedium, there's one where a kernel of an idea clearly exists, yearning to sprout in a more professional picture.
