See a physio or a trainer to do it right, but in general explosive or percussive movements are supposed to be good for knees. People used to think that jogging was terrible for knees, for instance, but now the consensus seems to be the opposite.

Starting slow and doing good form squats and slow burpees could improve your knee health to the point where you can do regular-tempo burpees. However, don't get medical advice from internet forums.