Side effects of adult DPT how long do they last?

Depends. Depends upon the side effect. A fever may last 1-2 days. Soreness can generally last up to 4-5 days if severe.
Tdap reactions. The tetanus-dipththeria-acellular pertussis vaccine often causes soreness and swelling at the site of the injection. Fever is also a possibility. The redness can be quite extensive. Generally these side effects clear up in a week or less.