Guys, thanks for your replies. So this company is my friend's company and he said to do it whatever way I like. He just doesn't want to have problem with accounting or when filing taxes. We are both unaware how the system works.

Besides he being my friend the relationship is that I am a seasonal contractor, not exactly a W-2 employee. I also possess the company's debit card which my friend would prefer to use, because it is simple and straightforward. But if I can just pay for the flights with my cc, get points, and then (legally) get reimbursement from the company in form of cash, I would prefer that.

So if this is ordinary and possible, what is the paperwork we need? Anyone knows?