I don't know many other aspies but I am one, and my friends, both boy and girl, often say I'm good at complimenting girls. Boys often ask me for advice too . It probably stems from my family being mostly female. But anyway:
1. Focus on non sexual things. Trust me, it makes misunderstandings less likely.
2. Focus on what is pretty about her. You know: smile, hair, eyes, new clothes, voice etc. I haven't found a girl who isn't attractive in some way.
3. If she is so pretty that you can't decide what to compliment on. Or you find being specific too embarrassing. Just be general, E.G You look pretty today. It's simple, It's probably overused, but It always works for me.
4. Say it naturally, trust me, I often observe my fellow men trying out their 'pickup lines' with that special 'pickup line' voice. It sounds wrong and it doesn't work.
5. Just say it, if it's embarrassing find a friend who happens to be female, explain the situation and ask to practice. The more confident you sound, the better it will work. A trick I use is allow my aspieness to take over, and say it frankly, while ignoring social cues . As long as you know her reasonably well it should work.
Finally, I'm not a flirt, I don't pick up girls, I just like seeing girls smile. My advice may only work for me. Maybe I'm just good looking. But as far as I know, my ways make girls smile, and as far as I know girls like boys who make them smile. So try them.
P.S If anyone disagrees with my advice, do tell. I love suggestions, and I love to learn new ways to compliment girls, as I said, I love making girls smile. It's my thing.