At what age is it safe for children to transition out of a cot on to a flat mattress on the floor.

Red Nose recommends that you move your child from a cot to a bed when they have attempted to climb out of their cot & look like they will be successful.
This usually occurs between 2yr - 3.5yrs but may be as young as 18mths.

A child no longer sleeping in a cot has greater access to all living areas. Before your child graduates to a bed, check your child’s room and throughout the house for possible hazards.
https://rednose.org.au/article/making-your-home-safe-before-moving-a-child-from-a-cot-to-a-bed

Red Nose has a number of resources in relation to cot to bed safety, including
https://rednose.org.au/article/where-to-sleep-a-child-who-has-moved-from-a-cot