Yes a broken angle can lead to amputation if there is an infection.
However most cases of broken ankles are not serious enough to where they lead to amputation but it can in rare cases happen.
As long as the broken ankle is fixed promptly and fixed correctly and you avoid any walking on the broken ankle while it heals there should be no need to amputate.
When you get an infection and the infection is not treated and the infection gets serious enough then you would need amputation.
But many kids, teens and adults get broken ankles yearly and hardly any amputation happens.
If the broken bone is not set right then a serious infection called osteomyelitis can happen which then if left untreated can cause amputation to be required.