How long does hydroquinone 10% + kojic acid 4% + tretonin 0.1% + steroid cream takes to work?

That is a strong combination topical product for the treatment of melasma. I usually see results with lightening creams at the 4 week mark. If you are getting red and dry with application, consider applying a moisturizing cream 1-2 minutes after the application of the lightening cream.

My melasma program last for 10 weeks, so at week one, you should not be having these side effects- possibly the HQ at that concentration is causing irritation. I suggest you speak to your dermatologist about titrating the dose. Melasma can not be completely cured, however effective treatment are possible. This is because your skin is extremely sensitive to UV and even the smallest amount can stimulate your pigment cells to produce colour. The mainstay of treatment is strict UV protection- hats, sunglasses and SPF every 4 hours. 
I prefer to use a combination of creams and laser for melasma. Hydroquinone can be used (5-8%), along with vitamin A creams. I usually start my patients on laser (low dose Q switch or Picosure) a few weeks after they commence on creams. Another laser I use is the Clear and Brilliant in the Permea setting combined with creams. 
In some cases I combine glycolic AHA peels, and in other cases I use a tablet called Tranexamic acid to help. Melasma treatments should be tailored to each patient. 
All the best, Dr Davin Lim. Laser, surgical and aesthetic dermatologist. Brisbane, Australia