I'm so sorry about your fiancé's sister.
I haven't seen vases of flowers at funerals in the UK - just wreaths. And at the funerals I've been to, there haven't really been flowers. Most people seem to prefer to donate money to a charity instead these days. That's not necessarily what your fiancé's family is doing, however. Can you have a word with him and find out if they're asking for donations rather than flowers?
As for churches vs. funeral homes, all the services I've been to in the UK have been at a crematorium, never in a church. But again, my family might be different from your fiancé's. I think you do need to have a chat and ask him some of these questions.
Perhaps sending some condolence flowers to his parents might be nice, if there aren't going to be flowers at the service. You might try
Interflora; they have some beautiful sympathy vases.
Again, I'm really sorry.