The first that cinema audiences knew of Owen Kline was his wilting, damp-eyed performance as a 12-year-old in Noah Baumbach’s spiky divorce comedy The Squid and the Whale. Kline played a Brooklyn boy who responds to his parents’ separation by wiping semen on the books in the school library, creating what you might call the Gooey Decimal System.

Now 30, he has written and directed a debut film that is no less sticky, uncomfortable and grimly hilarious. Funny Pages follows Robert (Daniel Zolghadri), a gifted high-school cartoonist, as he rejects his privileged upbringing, moves into a squalid basement with two unsavoury middle-aged men, and develops an attachment to Wallace (Matthew Maher), who has anger-management issues and prefers not to be reminded of his abortive career in comics. Robert is convinced the older man is a neglected genius, whereas the evidence suggests he has hitched his wagon to a plummeting star.

Kline, who harboured his own youthful dreams of becoming a cartoonist, knows the comic-book world intimately. “I was the kid in the store looking for that one long box of underground comics,” says the baby-faced director on a video call from his cluttered office in Queens, New York.

His adolescence was full of lo-fi, DIY exploits. He drew comics, made CDs of his own prank phone calls and befriended the late Chris Sievey, AKA Frank Sidebottom, on Myspace. “He’d write sweet messages on my wall and post pictures of himself in the mask doing funny things,” he says. Kline also played in “obnoxious novelty bands” who put out vinyl singles with handmade covers. “We’d be cutting and gluing and Xeroxing. It was a good lesson in how to inject personality where there isn’t money.”

Even The Squid and the Whale was a low-budget quickie shot on handheld 16mm and stripped of showbiz glitz. Kline went straight back to school after making the film in the summer holidays and ignored the scripts that flooded in when it became a surprise hit. “I never wanted to be in the industry,” he says. “Being a child actor seemed a hellish path, and a quick way to embarrass yourself.”

By 15, he had become a familiar face at punk joints, repertory cinemas and comic-book dives. A kind of indie It-boy, he was mentioned alongside the teenage Zoë Kravitz in a New Yorker piece about the East Village. The magazine described him as one of the city’s “young moderns … tall and handsome, with big feet, a round face, and dark eyes”. It noted that he “lives with his parents uptown and hopes to be a director”.

Those parents are Kevin Kline, who won an Oscar for A Fish Called Wanda, and Phoebe Cates, the Gremlins star who retired from acting 20 years ago. His sister is the musician Greta Kline, while his late maternal grandfather, Joseph Cates, was a US TV producer as well as the director of the sleazy 1965 thriller Who Killed Teddy Bear? starring Sal Mineo. So when Kline tells me about the travails of getting Funny Pages made, and how it took 10 years of frustration, misery and rejection, I warn him that people will be sceptical. One Twitter user, for instance, described him as “a third generation nepo baby on both sides of his family”.

“But nobody treats you seriously!” he protests. “Like, maybe if somebody knows somebody then maybe you can get a script to them. That doesn’t mean they’re gonna read it. No one wants to read someone’s kid’s ‘thing’. Would you? Imagine if your friend said: ‘Hey, my kid wrote a thing.’ Ugh. Whatever, it’s a sucky scenario to be in.”

Were his parents supportive? “So supportive. They wanted so badly for me to figure out a way to make my film.” The industry was less enthusiastic. “You get the meeting and they say: ‘I’m so excited for this, I’m going to read it right now!’ But they’re just trying to get you out of the room. People did not treat me or this project seriously. They thought it was juvenile and offensive. I tried my connections and failed, time and time again.”

That is, until Josh Safdie read Funny Pages and offered to produce it. Kline has known him and his brother Benny, the directors of Uncut Gems and Good Time, since he was in his mid-teens. They share a scuzzy but humane sensibility: he helped make an animated trailer for their 2009 debut, Daddy Longlegs, and acted alongside a monkey in their 2010 short John’s Gone. “Once the Safdies got involved, people understood Funny Pages through a different lens,” he says. Along with Ronald Bronstein, who directed the clammy, squirm-inducing Frownland, they worked with Kline on the script for several years.

“I’m a perfectionist,” he shrugs. “And everyone recognised that Funny Pages didn’t need to be forced into a traditional production schedule. So many hack producers rush these little indies so they can shove them into Sundance. Then the result is undercooked because they didn’t figure out what it was. That’s most people’s first movie.” His had time to mature. Or rather: “It was nurtured like a sick baby under a rock.”

The extended gestation allowed him to build the characters with his cast members, some of whom he has known for years. As Robert’s chirpy best friend, the first-time performer Miles Emanuel (“I don’t like the term ‘non-actor’,” says Kline) is winningly authentic, possibly because he is playing a version of himself. Kline met him when Emanuel was an 11-year-old customer at the video shop where he worked. “He came in with his babysitter and rented Bergman’s Hour of the Wolf. I thought: ‘Is this babysitter paying attention?’ Then I discovered Miles was working his way through 1001 Movies You Must See Before You Die. I’d recommend something low-brow to him, and he’d be, like: ‘It’s not in the book. It’s not in the book.’”

Whether Funny Pages will make it into future editions of the book remains to be seen, but it has not been short of devotees since premiering at Cannes. Sean Baker, director of The Florida Project, called it “fantastic” and “full of genuine LOL moments”. Terry Zwigoff, whose films Crumb and Ghost World are pinnacles of comic-book cinema, declared it “a sick, nightmarish journey akin to a bad acid trip”.

When I catch up with Kline in London a few weeks later, he is chewing on jelly beans to boost his blood-sugar levels and seems astonished by the rave reviews. “I wrote the movie as a comedy that was acerbic enough for my friends to enjoy,” he says. “I didn’t care if anybody saw it. So I’m shocked.”

Audiences seem to identify strongly with Robert’s misdirected idolatry. Was there a Wallace in Kline’s own life? “Oh yeah,” he says. “I’ve butted up against a lot of brilliant, creative people who I thought were geniuses, and who have dealt with their own mental-health issues and self-destruction by taking it out on me and others.” Robert, though, is only partly a self-portrait. “He is striving in this optimistic way for pessimism. He’s running toward failure.” Unlike Kline, who is moseying in the opposite direction.

• Funny Pages is in cinemas and streaming on Curzon Home Cinema from 16 September.