I'm thinking of flying across the country for sex when I'm seeing someone else but it's not serious
Are you wanting to start a relationship with this person?
Not necessarily, he is just some random fuck, I'm not in love with him
You are expected to be monogamous in a relationship, so before you fly across the country you should ask your other partner if it's fine with them.  If you don't want to end up getting dumped, you should reconsider what your planning on doing.
Eh, they are just a fuck buddy and they can't be serious.
I still think that that is something that you should discuss with your current partner. When you are in a relationship, you are expected to only have relations with that person.