The phrase "a kind of summary" is correct and usable in written English.
It can be used when you want to describe something that serves as a summary but may not be a complete or formal summary.
Example: "The report provided a kind of summary of the key findings from the research."
Alternatives: "a sort of overview" or "a type of recap."
Summer, for me, so often becomes a kind of summary — it's the season I most easily, and most happily, forget.
Ms. Goddard offered a kind of summary: "Pink roses climb archways in summer, a putto pokes through yellow roses, and in the fall the maple trees change color".
From it she copied out some of the most important facts to make a kind of summary of her father's life for herself and her mother.
"It's choice, not chance, that determines your destiny," Mrs. Nidetch was often credited as saying, a kind of summary of Aristotelian ethics.
The Michelin inspectors, gloomy middle-aged men eating alone, used to be indistinguishable from the other gloomy middle-aged men eating alone, and their stars were a kind of summary of the opinions of all those tired travelling professionals.
On the other hand, the art of today would not exist without the art of the past – everything that we are now is a kind of summary of all that has gone before.
It's a pretty epic rant that any kind of summary here won't do justice, so I'll just suggest listening to it.
It takes weeks to read, weighs as much as a Sunday roast and might do real harm if thrown from a moving vehicle or hurled (as impatient readers may wish to do around the 700-page mark) willy-nilly from an upper-storey window.There is no plot as such and what story there is resists any kind of summary.
The New Deal legislation itself is dealt with in a kind of quick summary.
Finally, at the very front of the magazine there is a kind of executive summary of our best articles called "readme". Each "readme" ends with a call to action: we tell you what you should do.
In "A House for Mr. Biswas," the Wounded and the Wounder are hard to disentangle, and Naipaul often adopts a kind of cool, summary omniscience that he uses to provoke our rebellious compassion.
