Christian and Quincy Combs, fired off a cease and desist letter to a guy named Courtney Burgess and his attorney Ariel Mitchell over "Kim Porter Tell It All ('Tell It All')" ... a book currently sold online under the pseudonym Jamal Millwood.

In the letter, obtained by TMZ, the Combs bros say they became the rightful heirs and owners of Kim's intellectual property rights following her death in November 2018 ... and therefore her purported diary entries belong to them.

As they point out ... Burgess himself did a bunch of interviews to promote the book, claiming it was an "original unedited" copy of her diary/memoir. He's alleged he got a flash drive from people who were close to Kim, and printed it without any edits to produce the book.

Quincy and Christian are shooting down that narrative, saying the whole flash drive tale is "patently false" and misleads the public. But, in the letter they add, IF it were true the flash drive would belong to them ... as Kim's heirs.

We spoke to Burgess and Mitchell a few weeks ago in NYC, where they told us they'd met with federal prosecutors. We're told the feds seized his phone, which contained a copy of the flash drive data used for the book.

Kim and Diddy's sons are now putting Burgess on the clock -- they say he has 5 days to shut down the online sale of the book, stop doing interviews making his false claims and turn over any of Kim's possessions he claims to have. They also want an accounting of any money he's already made off the book.