Burton posted on Instagram that his “heart is broken” and that “we had something so special” following the death of the TV presenter at the age of 40.
Alongside a photo of the pair, he wrote: “My heart is broken we had something so special.
“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 everyday.
“I love you with all my heart”.
A lawyer for the Flack family said that she took her own life on Saturday.
According to her management company, she had been “under huge pressure” since she was accused of assaulting Burton.
She had denied the charge and was due to stand trial next month.
Flack’s management company has criticised the Crown Prosecution Service (CPS) for pressing ahead with what it called her “show trial” even after Burton said he did not support it.
The CPS responded: “Given the tragic circumstances, we will not comment on the specifics of this case at this stage.”
Tributes have poured in for the ex-Love Island host after the tragic news broke on Saturday.