Sources familiar with the situation tell TMZ ... Kim and her team of high-powered attorneys are now inundated with letters, calls, emails and social media messages from people who are incarcerated, or the relatives of prisoners. We're told they're all seeking help to get released.

It's no secret why. TMZ broke the story ... Kim successfully helped release 17 inmates in the last few months by funding the 90 days of Freedom campaign -- which is spearheaded by lawyers Brittany K. Barnett and MiAngel Cody of the Decarceration Collective.

The people they've been helping are inmates who were serving unduly long prison sentences -- many of them life -- for low-level drug offenses.

Barnett and Cody are utilizing the newly signed First Step Act as grounds for the releases.

We're told Kim receives hundreds of letters each week -- not to mention the flood of letters and calls made to the attorney's offices as well -- and those numbers don't even come close to the social media tags Kim gets.

To be clear, this is not a rubber stamp process. On the contrary, our sources say Kim is setting aside time each night to sift through many of the inmates' stories -- and Brittany and MiAngel are doing the same. If Kim sees a case she feels strongly about, she brings to the team for further research.

When Kim started her mission, inmates referred to her as "The Princess of Prison Reform" ... we're told that nickname has stuck too.

TBH, since our post about Kim and the 90 Days of Freedom ... our own office phones have been blowing up with people trying to get in touch with her for prison help.