I have created a matplotlib layer for AWS lambda using docker following these steps:
sudo docker pull amazonlinux
sudo docker run -it amazonlinux:latest /bin/bash
# inside container
yum -y install python37 zip
python3 -m venv python
source python/bin/activate
pip3 install matplotlib
deactivate
rm -rf python/{bin,include,lib64,pyvenv.cfg} python/lib/python3.7/site-packages/{__pycache__,easy_install.py,numpy*,pip*,pkg_resources,setuptools*}
zip -r aws_lambda_python37_layer_matplotlib.zip python/
# in other terminal, copy file from container to host
CONTAINER_ID=$(sudo docker ps|grep amazonlinux|cut -d " " -f1)
sudo docker cp ${CONTAINER_ID}:/aws_lambda_python37_layer_matplotlib.zip .
# exit container
exit
Note that this script deletes numpy from the layer which is necessary due to size restrictions of a single lambda layer. So you will need to enable the official numpy/scipy layer from AWS in your lambda function as well.
You can also do this without docker on a small EC2 instance. You can find the resulting zip here: https://github.com/ttor/aws_lambda_python37_layer_matplotlib