The tennis player had been in a relationship with the former Love Island host.
On Saturday, Flack was found dead at her London home, her family said.
A lawyer for the family confirmed that Flack took her own life, aged 40.
“We would ask that the press respect the privacy of the family at this difficult time,” a family spokesperson said.
Now, Burton has issued a statement regarding the new on Instagram.
“My heart is broken we had something so special,” the 27-year-old wrote.
“I am so lost for words I am in so much pain I miss you so much I know you felt safe with me you always said I don’t think about anything else when I am with you and I was not allowed to be there this time I kept asking and asking.
“I will be your voice baby I promise I will ask all the questions you wanted and I will get all the answers nothing will bring you back but I will try make you proud every day. I love you with all my heart.”
Flack began her career on ITV’s Bo’ Selecta! and went on to present a variety of shows for the broadcaster, including spin-offs from I’m A Celebrity... Get Me Out of Here! and The X Factor, as well as Love Island.
She left Love Island before the current series, after allegations of assault against Burton.
Flack’s management on Saturday criticised the Crown Prosecution Service for pressing ahead with her “show trial” even after her boyfriend said he did not support it.
If you or someone you know is struggling with mental health, you can reach out for confidential support at Samaritans by calling 116 124 or visiting their website