It might also be that the plastic button is misaligned or presses too much (continuously) on the flex button. The only way to know for sure is to test the flex button itself first.
If the flex button is broken and it's difficult to replace then in the past I've taken the metal dome off, cleaned the contacts and surface beneath it reapplied it. It requires a bit of finesse and steady hands.
Unsoldering those buttons without melting them is almost impossible. Usually the best course of action is to replace the entire assembly (like shown in the video).