I have severe sciatica, how do I reduce the inflammation when it flares up?

See Your MD. Firstly, your "sciatica" as you are referring to is a distinct medical term that refers to compression of the nerves that make up the largest nerve in the body known as the sciatic nerve. Many people use this term to explain back/leg pain incorrectly. I would see your doctor for a thorough work-up that should include a MRI if you have having leg pain/weakness/numbness.
Core Exercises. Typically core strengthening exercises are the best to help relieve pressure and forces in the spine. I would try and google some or look them up on youtube to see descriptions. If you can do them yourself, wonderful otherwise ask your doctor to get a referral to a good physical therapist for further assistance.
Steroid. Go to your doc - usually will prescribe short course of steroid such as Medrol (methylprednisolone) dosepak for a week and possibly additional pain killers and/or muscle relaxants. You will also need xray and perhaps MRI if persistent to make sure you do not have herniated disc that needs surgical fix. (chrisohmd.Com).