Linear Discriminant Analysis (LDA) before or after k-fold cross-validation?
It depends on what you want to achieve.

If you want to visualize the results of your SVM classification, then you should do it after.

If you want to reduce noise, speed up training ... or whatever reason you want to reduce the dimensionality of your problem. You should do it before. 

One idea here that can be useful, is to do LDA inside a pipeline and choosing the best hyperparameter within the CV. 

In this example you can check a PCA and then a logistic regression. Your case will be similar but with LDA and SVM.