Tinkler was Team GB's youngest medallist at the Rio 2016 Olympic Games when she earned a surprise floor bronze as a 16-year-old but announced her retirement from the sport, aged just 20, earlier this year.
In a social media post, the 2015 World Championship bronze medallist also indicated she had submitted a formal complaint to British Gymnastics last December but was yet to have "any feedback or outcome".
Tinkler's revelations come amid widespread allegations of abuse at all levels, and concerning all ages, within the sport in Britain.
"I'm heartbroken by the stories that have been told over the past week," wrote Tinkler. "I'm so proud of my fellow gymnasts who have shared their stories.
"I know how hard it is and your bravery has been a shining light and inspiration in dark and troubling times for the sport we love.
"I submitted a formal complaint to British Gymnastics in December 2019. It was an account of my experiences as a club and elite gymnast, and the experiences I shared were the reason for my retirement in January, not a physical injury as was suggested by some at the time.
"After eight months, I'm no closer to having any feedback or outcome. It took a lot of support and counselling to build up the courage to tell my story. I hope someone now listens to us."
British Gymnastics have recently announced the launch of an independent review into accusations of abuse in the sport, which will be conducted by Jane Mulcahy QC.
And they released a statement to media outlets in response to Tinkler's post.
It read: "British Gymnastics received formal notification of a complaint from Amy Tinkler in December 2019 and she provided full details of this complaint to us on 10th March 2020 which then allowed the investigation to proceed.
"It is at an advanced stage and we have kept Amy Tinkler fully informed and provided her with the appropriate support and we will continue to do so.
"We can make no further comment at this stage in the process."