It is not possible to run node red without installing it.
Unless, that is, you have an identical system and make a clone of the disc and put that into the new system. Depending on your OS that may work. For example if you were running on a Pi then you could make an image copy of the card, move that to another Pi of the same type.
I believe another possibility may be to build your system into an installable package with node red, which then allows you to install node red with your flows in one go. I believe electron-node-red does something like that, but you said that isn't what you want.