How long does it take for a thigh lift scar like this to start fading and going down?

Surgical scars need time to heal and fade. You are only one week post op! At this point it is hard to determine what the scars will look like in 2 months time. Listen to the advice of your surgeon regarding caring for the incision site. 

Thank you for your question.  Cscars can take six months to a year to flatten and fade completely but it is likely the yours will start settle in a few months.    When in doubt checked in with your plastic surgeon to make sure nothing else is going on.  It's an infection could not be diagnosed here but I don't see any sign of it.  Best wishes.  

First of all, congratulations on your thigh lift.
As with any surgical scar, it takes some time before they fade and heal. In general, these scars fade into a whitish line in a span of one to two years. However, scars from arm and thigh lifts are notorious for being rather stubborn and noticeable, so you can’t expect a massive improvement within two months of your surgery.
Regarding infection, you have to watch out for the usual signs: redness, swelling, pain, tenderness, fever, and the presence of pus. Based on your descriptions and photo, it doesn’t seem that your wound is infected.
Since you’re just a week post-op, it is still hard to accurately assess your wound healing. Give it a few more weeks, and don’t forget to attend your follow-up consultation with your plastic surgeon.
Good luck!