If the boot heel cup presses on the tendon, that can cause damage to the tendon. If there is pressure, trash the boots.
Think about what you do different in the boots, perhaps it is the activity and not the footwear.
Where does it hurt on the tendon? Pain down close to the ankle or up higher?
Stretching, despite what we have all been told for years, doesn't help tendons. Tendons like slow, heavy loading. For the Achilles heavy calf raises are the fix with a slow lowering phase.
If the pain is high, then full range of motion, dropping the heel below the level of the toes. Such as standard on the edge of a step
If the pain is near the ankle bone, dropping the heel below the toes compresses the injured area and is bad. So calf raises on a flat surface.
I worked through some left distal Achilles tendinitis this year. Still doing heavy calf raises to keep it away, and avoid resting the pack of my heals on hard surfaces.