8.1.2 is the latest version that's available in the RHEL repos for RHEL 7.6 (and also RHEL 7.8) for the corresponding version of Python which is 2.7. Version 19.3.1 is available but it's for Python 3.8. You can see it available if you enable the necessary RHEL repos and search for the package with yum:

subscription-manager repos enable rhel*
yum list available | grep python-pip

That will show you the latest versions for all of the available versions of Python including 8.1.2 for Python 2.7 and 19.3.1 for Python 3.8.

If you want version 21.x, then you need to install a later version of Python such as 3.8. Python 2.7 is no longer supported and won't receive anymore updates.

I was going crazy about the same issue. The reason why yum couldn't find python-pip was that it is not called python-pip anymore. Starting with EPEL Version 7 it is renamed to identify the python version. On my centOS machine i can find now the following python*-pip packages.

[root@asdasdasdasdsa ~]# yum info python*-pip
Loaded plugins: fastestmirror
Loading mirror speeds from cached hostfile
 * base: ftp.rz.uni-frankfurt.de
 * epel: mirrors.mit.edu
 * extras: mirror.23media.de
 * updates: ftp.plusline.de
Available Packages
Name        : python2-pip
Arch        : noarch
Version     : 8.1.2
Release     : 5.el7
Size        : 1.7 M
Repo        : epel/x86_64
Summary     : A tool for installing and managing Python 2 packages
URL         : http://www.pip-installer.org
License     : MIT
Description : Pip is a replacement for `easy_install
            : <http://peak.telecommunity.com/DevCenter/EasyInstall>`_.  It uses mostly the
            : same techniques for finding packages, so packages that were made
            : easy_installable should be pip-installable as well.

Name        : python34-pip
Arch        : noarch
Version     : 8.1.2
Release     : 5.el7
Size        : 1.7 M
Repo        : epel/x86_64
Summary     : A tool for installing and managing Python3 packages
URL         : http://www.pip-installer.org
License     : MIT
Description : Pip is a replacement for `easy_install
            : <http://peak.telecommunity.com/DevCenter/EasyInstall>`_.  It uses mostly the
            : same techniques for finding packages, so packages that were made
            : easy_installable should be pip-installable as well.

I run Centos 6.5 on Virtualbox and this command solved it.

# yum update
# yum install centos-release-SCL
# yum install python27

To install pip3.6 in Amazon Linux., there is no python36-pip. If you install python34-pip, it will also install python34 and point to it.

The best option that worked for me is the following:

#Download get-pip to current directory. It won't install anything, as of now
curl -O https://bootstrap.pypa.io/get-pip.py

#Use python3.6 to install pip
python3 get-pip.py
#this will install pip3 and pip3.6   

Based on your preference, if you like to install them for all users, you may choose to run it as 'sudo'