The \n gets parsed by Python into a literal newline. You can avoid that by using a raw string instead,
p = subprocess.run(
r'''echo -e 'FROM busybox\nRUN echo "hello world"' | docker build -t myimage:latest - ''',
shell=True, check=True)
but I would recommend running a single process and passing in the output from Python; this also avoids a shell, which is generally desirable.
p = subprocess.run(['docker', 'build', '-t', 'myimage:latest', '-'],
input='FROM busybox\nRUN echo "hello world"',
text=True, check=True)
Notice also how we prefer subprocess.run() over the more primitive subprocess.Popen(); as suggested in the documentation, you want to avoid this low-level function whenever you can. With check=True we also take care to propagate any subprocess errors up to the Python parent process.
As an aside, printf is both more versatile and more portable than echo -e; I would generally recommend you to avoid echo -e altogether.
This ideone demo with nl instead of docker build demonstrates the variations, and coincidentally proves why you want to avoid echo -e even if your login shell is e.g. Bash (in which case you'd think it should be supported; but subprocess doesn't use your login shell).
