I kicked my second toe onto the chair leg. Hurts and swollen. How long will it take to get well again?

Depends. Since you injured it, you really need an x-ray to determine if it is broken. Then a healing time can be predicted.
10 weeks. Whether you broke your toe or not, it takes about 10 weeks to get better. Look for 10% improvement per week. You should be 50% better at one month and 80% to 90% better at two months. If you are not improving then you should see a medical professional for evaluation.