This may be true, but bleach will not work to disinfect the soil in a run. Bleach is inactivated in the presence of organic matter, which all soil in a chicken run has plenty of. If you read carefully the information in the link, it mentions the bleach/vinegar solution as good for disinfecting all sorts of inanimate objects such as floors, countertops, equipment, etc,
Brian makes a good point too. As long as that is kept in mind, the other suggestions go a long way toward helping to prevent disease and parasite infestation.
Professional is correct ...
 This is why my run and coop floor are not of dirt or sand (coop floor is aluminium and run is paved).  
I am sorry but I think the risk of mixing the bleach with anything is simply too risky... (eventual damage to the lungs is irreversible and if on a windy day and carried to your birds who are a hundredfold most sensitive to irritants... just not worth the risk IMHO)
From Wikipedia (entry BLEACH):
Mixing sodium hypochlorite with acids like vinegar or drain cleaners containing sodium bisulfate (sodium hydrogen sulfate), or even lemon juice can release chlorine. Hypochlorite and chlorine are in equilibrium in water, the position of the equilibrium is pH dependant and low pH (acidic) favors chlorine,[1]
Cl2 + H2O  H+ + Cl- + HClO
Chlorine is a respiratory irritant that attacks mucous membranes and burns the skin. As little as 3.5 ppm can be detected as an odour, and 1000 ppm is likely to be fatal after a few deep breaths. Exposure to chlorine has been limited to 0.5 ppm (8-hour time-weighted average40 hour week) by OSHA in the U.S.[2]
IMHO if you have had a bout with an illness or simply feel it is time to for a change... move your coop to a different area if possible or else remove the top layer and replace with non-fine type of sand (can be easily removed and renewed and raked (removal of poo) regularly) > you will find a a (deep) layer of course sand also useful in that it will not retain water and become muddy like dirt.
... 
please do not start mixing chemicals unless you are a professional with appropriate safety masks etc... nevermind, just dont JMHO
http://chemistry.about.com/od/healthsafety/a/dangeousmix.htm
Common Household Chemicals - Dangerous Mixtures
Do Not Mix List
By Anne Marie Helmenstine, Ph.D.
"....Some of the common chemicals found in your home shouldn't be mixed together. It's one thing to say "don't mix bleach with ammonia", but it's not always easy to know what products contain these two chemicals. Here's are some products you may have around the home that shouldn't be combined. 
Bleach with Acid Toilet Bowl Cleaners
This mixture can result in toxic, potentially deadly fumes.
Bleach with Vinegar
Vinegar is a type of acid. Toxic chlorine vapor is produced. Don't mix chlorine bleach with any acid. Bleach with Ammonia
Toxic, potentially lethal vapors are produced.
Different Brands of One Type of Product
Don't mix different cleaners together. They may react violently, produce toxins, or become ineffective.
Highly Alkaline Products with Highly Acidic Products
Acids and bases (alkalis) can react violently, presenting a splash hazard. Acids and bases are caustic and may cause chemical burns.
Certain Disinfectants with Detegents
Don't mix disinfectants with 'quaternary ammonia' listed as an ingedient with a detergent. The effectiveness of the disinfectant may be neutralized. 
Chlorine bleach is sometimes called sodium hypochlorite or hypochlorite. You will encounter it in chlorine bleach, automatic dishwashing detergents, chlorinated disinfectants and cleaners, chlorinated scouring powder, mildew removers, and toilet bowl cleaners. Do not mix products together. Do not mix them with ammonia or vinegar. 
Read the labels of products in your home and following instructions for proper use. Many containers will state the most common dangers from interaction with other products....."