My implementation of string kernel from article H. Lodhi, C. Saunders, J. Shawe-Taylor, N. Cristianini, and C. Watkins. Text classification using string kernels. Journal of Machine Learning Research, 2, 2002 .
As far as I know, there is no implementation of this algorithm in scikit-learn.
Also you can look at http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/#libsvm_for_string_data for libsvm implementation of string kernel (with no warranty).
svm.SVC is a basic class from scikit-learn for SVM classification. It uses one-vs-one approach in multiclass case.
FILES: stringSVM.py - basic algorithm from the article
stringSVM_K2.py - algorithm with K''() from the article. Though authors say that algorithm with K''() is faster, in my realization, it comes out to be slower than basic algorithm. I suppose because of bad recursion support in Python.
CONCLUSION: Algorithms offered in the above mentioned article (pp. 424 - 426) are slow. Recursive realization leads to extensive memory usage (depth of recursion is achieved pretty soon). Caching helps not but so much as desired. There is a well-known problem with tail recursion in Python.