Sorry for the bad title, but I have identified co-expressed gene modules using the WGCNA-package. And it gives you a dendrogram showing the module colors. Like this:

I would like to create somehting like this, where the gene expression of the different samples are shown as a heatmap, with genes ordered in the same way as the dendrogram. Like this:

But I am not sure how I should proceed with this. Any advice will be greatly appreciated!

You can create a heatmap with genes shown in the same order as the dendrogram. You have already created a dendrogram before creating the first plot with the plotDendroAndColors function. The dendrogram contains a list element with the ordering of samples from one side of the dendrogram to the other side. Simply order the rows of your gene expression matrix in the same order as the dendrogram and plot it with heatmap.2. You must set Rowv to FALSE to prevent heatmap.2 from changing the order of genes in the plot.

library(gplots)
expressionMatrix <- expressionMatrix[dendro[["order"]], ]
heatmap.2(expressionMatrix, Rowv = FALSE, Colv = FALSE, dendrogram = "none", trace = "none")