Just a quick thing that got me up and working was to go directly to this webpage to download the latest pyserial3.4 here ( https://pypi.python.org/pypi/pyserial/3.4#downloads ) and doing a manual install got that working.
It seems that there’s something wrong with the update URL http://pypi.python.org/simple/ from the error message.
Please don’t confuse the pyserial version with the python version.
BrewPi is still python 2. You link to a python 3 package.
For an easier deployment, considering using docker instead.
Sorry, I admit to not knowing much about python at all. But what I suggested above did add pyserial3.4 into my Python2.7 folder and got it working. I’m not familiar with Docker at all and found this workaround easy to fix the problem with the update URL being broken.