You can flex your legs while sitting in a chair facing forward, simply by moving your leg outward while keeping your foot on the floor and holding it there for a few seconds, then retracting it until your foot is behind you, then alternating to the other leg.
Interlocking your fingers and slowly flexing your wrists to the left and the right for a few minutes a day can help tremendously to increase flexibility and reduce arthritis pain in the wrist area.
For your upper back, you can stand upright in front of a table, then lean over and place your hands on the table and tuck your chin back toward your collarbone. Once positioned as such, lift your upper back upward and simultaneously take a deep breath. Hold that position for 5-10 seconds and then relax while exhaling. While doing this, lower your spine slowly as you move both shoulder blades forward as if toward each other. Repeat this exercise for 10-15 repetitions.
For the shoulders and middle back, start again from an upright position standing as straight as you can, reach back and lock the fingers of both hands together. Breathe slowly and deeply and lift upward with your shoulders while at the same time, exhaling. Be sure to keep your chest up and your chin in. Repeat this for about 10-15 sets.
For the shoulders and upper chest, choose a free corner of the room to stand in and place your hands on the opposite sides of the corner. Take a step back about 18 inches from the corner. You now should be facing the corner directly with your hands on both of the walls with your body some distance from the wall itself. Keeping your chest up after inhaling, lean in toward the corner while exhaling. Repeat this exercise for 10-15 sets.
Whatever exercise program you choose, be sure to breathe properly when exercising. Oxygenation is important to any exercise regimen as it promotes a healthy heart rate and reduces fatigue; additionally oxygenation helps circulation, which is vital to achieving the flexibility and strength that you are trying to achieve in battling arthritis.
Also, listen to your body. It is natural to feel a little fatigue and soreness when starting a new exercise regimen, However if the pain of soreness persists for more than one hour, or you have a decrease in mobility that lasts longer than an hour, then the regimen should be reduced until the soreness desists.
Also, look for signs of increased swelling of joints or any persistent increase of weakness; these are signs of activities that are too strenuous and a reduction in activity will be necessary. Just remember to take all new exercise regimens slowly at the start. The idea is to increase flexibility not train for the Olympics.