I am a podiatrist, I’m all for mobilising joints but increasing mobility in the foot will in theory create a flatter foot, it probably won’t but just a thought.
Specific foot and lower leg strengthening will be of overall benefit to you but to specifically assist in your knee complaint it is unlikely that this will have much influence on it. And any changes in your arch height due to strengthening would be quite hard to observe visually, and anyway don’t worry about your flat feet, flat feet are normal, function of that flat fleet if leading to injury of your knee does not necessarily mean that it is not normal but it can be targeted with orthotic therapy.
Whatever your doing with altering your foot shape/arch by air squatting, I would stop or reduce this, your are loading structures in the foot that can’t tolerate this thus creating a problem.
1) Accurate diagnosis of knee problem and specific intervention to target the injury if not already done.
2) Low dye tap foot and see of any benefit; This will reduce pronation of your foot and thus may give more of indicator wether lower limb biomechanics are influencing your knee complaint
3) If you are standing in one spot for a number of hours, my view is that humans were not suppose to do this & definitely not suppose to be standing on hard surfaces such as concrete so I would consider more cushioned/shock absorbing shoe and or shock absorption mats to stand on.
Hope this helps.