Child is strep carrier, augmentin (amoxicillin and clavulanate) did not work. Would 10 day supply of clindamycin work?

Work for what? Being a strep carrier is not the same as having an infection. Normally no antibiotics are necessary and may even cause problems (like thrush, diarrhea, etc.) a good review of the subject is at: http://www.Pediatricweb.Com/madisonpeds/article.Asp?Articletype=9&articleid=851.
STREP CARRIER. Ten day course of Augmentin (amoxicillin and clavulanate) in adequate and oroper dose should be able to cure the strep carrier in most cases, but if culture of throat still shows strep without symptoms then it may be ok to take 10 day course of clidamycine in the appropriate dose.