This nice article describe very well how to install minishift on Windows, MacOS and RHEL: Hello World!
Unfortunately, there is no procedure for Fedora, can you provide some guidelines?
It is possible to download the CDK (minishift) binary directly from download page. You just need to be registered.
Next, you should configure your system environment (ie. set up hypervisor driver), take a look here.
Make the downloaded CDK binary executable:
chmod +x cdk-x.y.z-minishift-linux-amd64
Finally, you can continue with setting up the cdk binary as described in section 2 in Hello World page. Mainly, this is about preparing minishift configuration for proper hypervisor (as user can use more than one):
./cdk-x.y.z-minishift-linux-amd64 setup-cdk
or
./cdk-x.y.z-minishift-linux-amd64 setup-cdk --default-vm-driver xxx
in case that you are using different than default hypervisor (kvm on linux, could be virtualbox).