I just refilled my spa water and I am switching over to chlorine (nature 2 cartridge). I shocked last night with sodium dichlor and I guess I put too much in. My fc reading is 7. How long does it take to burn some off and do I need to lift cover to burn off quicker?

If you don't have an ozonator and don't have any bather load (i.e. don't use the tub), then the chlorine level will probably drop at a rate of around 25% per day, so from 7 ppm to 5.2 to 3.9 to 3.0 from one day to the next. If you have an ozonator, then the chlorine level will probably drop around 50% per day so from 7 ppm to 3.5 ppm to 1.8 ppm to 0.9. Yes, having the cover off will probably have the chlorine drop somewhat faster, but will also have your temperature drop as well or heating costs go up.

While high, the FC of 7 is not unusable unless you object to the "fresh chlorine bleach-like" smell you will probably notice.

If you wanted to lower the FC level faster, an easy way to do that is to use 3% hydrogen peroxide. The volume you would use would be the same as would generate that amount of FC using 6% bleach so you can use The Pool Calculator to calculate this. For example, in a 350 gallon spa, if you wanted to drop the FC by 4 ppm to get to 3 ppm, then that's 2.9 fluid ounces of 6% bleach so you would use 2.9 fluid ounces of 3% hydrogen peroxide to lower the FC by 4 ppm in 350 gallons.