I have been reading quite a lot of resources out there and have also
been experimenting on my own, but I couldn't figure out what is the
best way to do so.
Here is the scenario implying Alice and Bob working together on the
same feature:
Alice starts the feature branch:
  git flow feature start blah
she does some work there
  ...
  git commit -am "did some work"
Bob steps in. At this stage, I see two possibilities:
1/ local branches
Bob pulls the branch from Alice
  git flow feature pull alice blah
He does some work
  ...
  git commit -am "fixing some issues"
Alice to pull the branch from him to get his changes
  git flow feature pull bob blah
2/ remote branches
Alice needs to publish the branch
  git flow feature publish blah
Bob can then track and checkout the branch
  git flow feature track blah
  git flow feature checkout blah
He can work
  ...
  git commit -am "fixing some issues"
He pushes his changes
  git push
Alice can get them
  git pull
or
  git flow feature pull origin blah

Which is best to go with?

I am also wondering about the finish.
At the end Alice finishes the branch to have it merge to develop.
  git flow feature finish blah
But then, the branches still exist on origin and an Bob's machine. How
do we get rid of them?

Thanks.

As long as all team members can pull from everybody else's local repo then
opt 1 is fine, but if you have some team members who can't pull directly
then you should go with option 2. Perhaps some on your team is in a remote
location, firewalled, etc, but they do have access to a central server,
then to be consistent, you should share branches via a central origin repo
instead of direct pulls from developers local repos. If you try to use both
options at the same time for different developers then things will get
confusing.

For deleting branches after finishing a release or hotfix. Just make sure
Bob's repo has pulled from Alice (or from origin after Alice pushed to
origin) so the latest commits and has the merge with the master and develop
branches, Bob can simply delete a that feature branch, as in:
   git branch -d blah

You can also delete the branch on the origin repository if needed:
   git push origin :feature/blah

Note the empty space before the colon; that indicates you are pushing
nothing to the origin's feature/blah branch, effectively deleting it.