The Whites managing director was writing for the first time since calls for an independent regulator and transfer levy emerged following the publishing of the report.
Former sports minister Tracey Crouch, who led the review, described Kinnear's complaints at two of the 47 recommendations set out as a "tad extreme".
Kinnear said there was 'much to applaud' in the review of the game's governance though took issue with the call for independent regulation and an increased transfer levy to push further funds to the rest of football's pyramid, calling them as 'flawed as they are radical.'
He used 'The Great Leap Forward' - a campaign implemented by Chinese Communist Party leader Mao Zedong around 60 years ago, which led to the largest famine in human history and the deaths of millions of people - as an example.
“These proposals have been conflated to address the very separate issues of the demise of Bury, the threat of the European Super League and the takeover of Newcastle United," Kinnear wrote.
“Football is a private sector business and has flourished that way. Enforcing upon football a philosophy akin to Maoist collective agriculturalism (which students of ‘The Great Leap Forward’ will know culminated in the greatest famine in history) will not make the English game fairer, it will kill the competition which is its very lifeblood.
“Teams further down the pyramid do not need their means artificially inflated, they need to live within them.
Crouch, in response, told BBC Sport: "My report merely wishes to see more money going to grassroots, ensure that football clubs don't go bust, put diversity on the agenda and give fans a say on key issues. Maoism killed millions and millions of people."
Kinnear also drew criticism from former Manchester United defender turned pundit Gary Neville on social media.
The Football Supporters' Association voiced their concerns saying Kinnear had "undermined" the recent report.
Palace chairman Steve Parish and Aston Villa chief executive Christian Purslow have also recently criticised elements of the recommendations which were summed up in 10 ken points.