In my last relationship (which was the best ever for me), we were friends first. We spent the first 50 or so communications (emails and phone calls) talking about nothing but science, motorcycles, and V8 engines in pickup trucks. After we met and spent a few times together in person, we started getting kind of flirty.
But I don't know if it's something you can set out to do - convert a friendship into a relationship. If the "chemistry" isn't there, I don't think it would happen for me. In my case, the chemistry was definitely there.
OTOH, in the second best relationship I've ever had, we were definitely strictly friends first. For a long time. In fact, I was married to someone else when we met. We all saw each other a lot (all three of us were in college together). Eventually, due to completely unrelated circumstances, my marriage ended. I had not seen my friend in quite awhile by that time, but I ran into him 6 months or so after the divorce, and we started hanging out together again as friends. One weekend we went to the beach. I don't know if it was the combination of sun, sand, and alcohol, or what, but it sparked something, we ended up in a relationship, lived together for several years, got married and were married for 8 years. Things didn't work out in the long run (he considered himself bisexual when we first met, but ultimately came to the realization that he was really only sexually interested in men), but since our relationship had always been about being friends, and the sex was secondary, we split amicably and are are still friends.