Photo: PA
The two jockeys died as the fire spread through the flats in Buckrose Court in Norton, near Malton, in the early hours of Saturday.
Neighbours said they believed Miss Wilson was the girlfriend of another jockey, Ian Brennan, who jumped out of a window at the three-storey block to escape.
Police have arrested a local man on suspicion of arson.
Alan Foster, a businessman in his 30s who owns the building, said he let the flat to Mr Kyne and Mr Brennan, who had recently moved to Malton from Dublin. Mr Foster said he thought the fire had started in a hallway.
Mr Kyne, from Ireland, was a promising apprentice jockey who had ridden 29 winners this season. Currently third in the apprentice jockey championship, he rode for the Irish trainer John Quinn, who runs a racing yard in Malton.
Miss Wilson, from Forfar, Scotland, was riding in her first season of professional racing for the trainer David Barron and had been due to ride her mother’s horse, Imperial Sword, at Thirsk on Saturday.
Mr Barron, who is based in Thirsk, North Yorks, paid tribute to Miss Wilson as a “tremendous” jockey.
“She was just at the start of her career and was only in her first year of riding as an apprentice,” he said.
“She joined me at the end of last year and had ridden three winners for me out of only a handful of rides. She was very good, very capable and had tremendous potential. Everyone in the yard is just devastated.”
Her parents, Margaret and Drew Wilson, were too upset to speak as they travelled from Forfar to North Yorkshire.
Mr Kyne was also due to have ridden on Saturday at Haydock, where jockeys wore black armbands and a 20-second silence was observed before the first race.
Thirsk and Kempton racecourses also staged moments of silence, and flags at York racecourse flew at half mast, while jockeys at Stratford donned black armbands.
Tim Fitzgerald, a trainer from Malton, said: “[Mr Kyne] was a really nice lad and was doing well for himself. He was talented and it looked like he was going to go a long way in his career.
“He moved here last year and was doing well and slowly making a name for himself. Tragically, we will never know how far he could have gone.”
Superintendent Steve Tarn, of North Yorkshire Police, said that a local man was arrested shortly after the fire was reported at 2.15am on Saturday.
He said: “A man has been arrested on suspicion of arson with intent. We are going to interview him to establish his involvement or not.”
He said that two men had been taken to York District Hospital suffering from minor burns and the effects of smoke inhalation.
One of the men, thought to be Mr Brennan, was discharged yesterday afternoon.
Supt Tarn said that there was substantial structural damage to the block of flats and that fire crews had to make the property safe before they could recover the bodies.
A spokesman for North Yorkshire fire service said that the fire was in the stairwell and top floor of the block, known as The Tannery.
Firemen used ladders to get in through windows and found two bodies in a top-floor flat. Around 20 other residents were evacuated from the block.
Martin Brown, 45, who lives in the block, said he was woken by the sound of the fire alarm.
“I looked out of the window and there were people screaming and shouting,” he said.
“As I ran out, somebody kicked the front door open and flames came out. People were jumping out of windows. A man jumped out of a window on the top floor and he landed at my feet.”
Two jockeys have been killed in a fire in a block of flats on Saturday. A map of England, with North Yorkshire in red.

At 0200 BST on Saturday a fire broke out in a three-storey block of apartments in Buckrose Court near Malton, North Yorkshire, England.  The two jockeys have been identified as Jamie Kyne, who was only 18, and Jan Wilson, who was just 19.  Both were described as promising young jockeys.

Two other men had also been taken to a hospital in York due to the effects of minor burns and smoke inhalation. One of the men has now been released from the hospital and the other man's injuries are not thought to be life-threatening.

A police investigation is currently taking place in the area and a man in his 30s living in the area has since been arrested on suspicion of arson with intent. North Yorkshire Police are going to interview the man and try and establish whether he was involved or not.

Kyne was due to ride at Haydock on Saturday afternoon, while Wilson was due to ride at Thirsk on the same day, while riding her mother's horse, ''Imperial Sword'' — and so both were staying in the apartment as a means of accommodation, as Jamie came from Ireland and Jan was from Forfar, Scotland.  "The family are devastated and Jamie was a star," Kyne's aunt said.  "They his parents are so proud of him.  At the moment they are just devastated and shocked."

David Barron, Wilson's trainer, paid tribute to her as "a tremendous jockey". He said: “She was just at the start of her career and was only in her first year of riding as an apprentice. She joined me at the end of last year and had ridden three winners for me out of only a handful of rides. She was very good, very capable and had tremendous potential. Everyone in the yard is just devastated.”