The question of your setting is basically find which change between treated gene vs control gene is closer acroos gene, right? In that case you need to measure the change between the group, then you measure the change acrross gene. Clustering log2FC is okay I guess but I think it will not show any direct relationship because 2 genes up regulation/down regulation can be caused by many things.
I think calculating correleation between 2 genes expression is better. Calculate using normalized expression from CPM function from Limma or EdgeR I forget or VST from DESeq2.
Why I think it is better? Correlation for expression of 2 genes basically check if gene A is affected by gene B or vice versa. If a gene is affecting another gene, it will affect both in control condition and in treatment condition. It means that no matter the condition, there would be an effect of gene A to gene B.