Yes, you can floss both knees at once.
Recommend having 2 people so each knee is wrapped at the same time. I do that with a couple of construction workers I work with.

Why are you taping?
What is the goal of taping?
Getting him out of pain is the first priority.
When applied properly tape on the skin can interfere with painful signals which are directed to the brain.
Manage symptoms first.
Stay pain free.
Compression
Buy slack to the area soft tissue mobilization to address the stiffness.
If you want help with it let me know.