I wet the awning
down and then spray on a mixture in a gallon jug/garden sprayer of water, dish soap and bleach (do a google on cleaning RV awnings and you will find lots of info on the mixture). Spray the awning
well with the mixture then roll up the awning and let it sit for about 10-15 min. Then unroll and rinse it off well. A long car washing brush makes it easier to reach & scrubbing off the tough stuff as does dropping the legs of the awning down as far as you can to be able to reach it all on both sides. Have had success with real tough stains with using a microfiber cloth will a bit of Vim on it.
Once clean if you put a really good vinyl protection product on it at the start of each year, it makes getting the mildew off much easier as does remembering to pull out & dry off an awning thats been put away wet... which is something I unfortunately never see to remember to do more often than not! ;-)