Hello there @adriaan.wakefield 
and welcome to Kinsta Community!
I’ve just tested this on my Windows 11 machine, and could install Node/NPM as well as Gulp within the devkinsta_fpm docker container (which runs on Ubuntu 20.04). Though I only tried to install them and don’t have any experiences to use them with my local sites (in DevKinsta).
You might want to try the same with the following steps to install them in that docker container:
-
open CMD to open the command prompt on Windows
-
In that Command Prompt window, you may want to enter to the
devkinsta_fpmdocker container with this command line:
docker exec -it devkinsta_fpm bash -
I then installed Node by following the installations steps (1-3) here
as we can seen from the screenshot above, I was able to install it, and can see the node -v and npm -v returned with their versions installed.
- I then continued to install the
gulp-cli( with-gparameter ) as shown here
and as we can see from the screenshot above, gulp was installed and I could run gulp -v that returns with the CLI version.
- After that I also followed the instruction there to run:
npm install gulp
as we can see from the above, the command seemed to be successful (and it created node_modules folder and the other 2 files: package-lock.json and package.json )
Hopefully this will help you to install Node/NPM and Gulp on your devkinsta_fpm docker container. 
Best regards,
Agus