You could transpose the entire song up or down on the fly in FL Studio pretty easily. Here's how.

Towards the top right of the main FL window, there's a Master Pitch slider... the one next to the volume slider, #10 in the image above. It moves up or down in increments of 20 cents. To change the song key to the next letter, move it 100 cents.

Applying key changes only makes sense with melody plugins. Percussion plugins don't need key changes. And if you try changing the key of a drum sound, it's very likely you will just distort that drum sound.

So you need to tell FL Studio which plugins to apply key changes too, and which ones not to apply. And for that reason, in the MISC tab in plugin Settings, you will find Enable Main Pitch toggle box. That toggle box can be found just above the virtual keyboard in the MISC tab.

For all plugins that are pitch-relevant, toggle that box on. For precussion plugins you don't want to be effected by master pitch change, disable that box..