The video shows TK MMA coach, Franky Spencer, reading Fury a poem he wrote about his boxing exploits.
Boxer Joe Parker also appears in the clip.
As Fury listened to the poem, which thanked him for visiting the gym, Daniel Kinahan watched on giggling, clapping, and chatting with others in the crowd.
Spencer, Parker and Fury all have no involvement in criminality.
It came after Irish influencer Niall Ryan shared a snap of himself posing with Fury and Kinahan at the gym on Instagram.
In recent months, Kinahan has made a habit of appearing in photographs with well-known fighters on social media as part of a carefully curated attempt at managing his image - often following a burst of bad publicity in the media.
In one snap, Kinahan could be seen pointing to a 'No Drugs' slogan on a tee-shirt with fighter Sunny Edwards.
Under the photograph, Edwards - who has no involvement in crime - wrote: "Always good to see an old friend."
The Liverpool-born fighter has been one of Kinahan's most vocal defenders and has previously described him as a "legitimate" businessman.
Bizarrely - and perhaps knowingly - Kinahan smiles for the camera as he points to Edwards' t-shirt which bears the caption: "No Drugs, No Champions."
Leading boxing writer Alan Dawson recently revealed how sources have told him Daniel Kinahan micromanages his appearances on social media.
US journalist Dawson - who is the combat sports correspondent for Insider magazine - made the comment after Kinahan recently posed for a number of photographs on social media.
According to Dawson, who is well-known for his investigations into Kinahan's involvement in boxing, that whenever Kinahan's name, or image, crops up “it's because he, specifically, wants it to”.
“He tells people what to say and is a micromanager in this game, according to sources with direct knowledge of his actions,” Dawson tweeted.
Tyson Fury has previously praised Kinahan for his role in guiding his career and publicly acknowledged the pair had worked together.
After a deal was done for Fury to fight Anthony Joshua in 2020, the Gyspy King took to social media to proclaim: "I'm just after getting off the phone there with Daniel Kinahan.”
"He's just informed me that the biggest fight in British boxing history has just been agreed."
In June 2020, Fury’s promoter Bob Arum announced that Daniel Kinahan was no longer working as Tyson’s advisor.
"Over the weekend I’ve had a lot of conversations with Tyson Fury and what we both decided is that myself, Top Rank and Fury will do all negotiations for fights in the future," he told the Daily Telegraph.
"Whether it’s for Joshua or Wilder or anybody else. We’ve informed Eddie Hearn about that. He knows where to go for the negotiations. Tyson and I have had long negotiations about it. That’s the way it’s going to be."
Kinahan continues to be supported by a number of boxers and fighters - even as he becomes increasingly isolated from the criminal underworld in Ireland.
Sunday World revealed how the head of the Irish mafia was said to be under increasing pressure as he spends his final days of freedom in Dubai while the law enforcement net continues to tighten.
Kinahan moves about with extreme caution in his Dubai bolthole, staying in different places every night and rarely seeing his wife Caoimhe Robinson as he tries to remain on the move while juggling a billion-euro drug empire on the verge of collapse.
While named in the High Court as a top-level drugs boss, Kinahan is yet to face charges for any crimes in Ireland.