Flex is normally designed to be used where it can be seen, and as such it does have a amp rating as under normal conditions it will not be covered in any way. And it is designed to flex hence the name, it has many strands of thin wire, when installation cable is designed to be fixed, so has less strands in each core, and once installed should not be subject to much movement, and since it may be covered will not have a fixed amp rating, you need to look it up.
I would not expect the wiring to thermostats to move, so does not need to be flex, and I would expect flex marked as 13A to be 1.25 mm² there is nothing wrong using flex instead of the stiffer twin and earth, in fact items like caravans have to be wired in flex as the chassis and body can flex so the cable has to flex with it, main reason for not using flex is it costs more.
With hydraulic UFH the cable to the thermostat does not carry much current, however with electric it often does, and it depends on the cold junction as to if the cable used actually gets warm during use, cable in general comes in three temperature levels 60°C, 70°C and 90°C flex is often rated at 60°C with so many variables no one can say yes or no as we don't know route or how close to the heating mat.
Some one needs to sign that they have designed, that person should select the cable to use.