While Amazon Linux AMI has yum as a package manager, it is not that all compatible with any RHEL or CentOS distributive. A lot of changes that AWS team brought into this image made it a separate distro, so no eyebrows should be given when battle-tested procedure to install python3 will fail on Amazon Linux. (Yeah, python3 does not come included yet in Amazon Linux)

Fortunately it is very easy to fetch (while not the latest release) python3:

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# list available packages that have python3 in their name
yum list | grep python3

# install python3+pip, plus optionally packages to your taste
sudo yum install python35 python35-devel python35-pip python35-setuptools python35-virtualenv

# update pip3. optionally set a symbolic link to pip3
sudo pip-3.5 install --upgrade pip

And that is it!