RVA, et al,
I have somewhat thick flabby arms but I wear sleeveless a lot. And while my sister (also thick like me) feels the way you do and tells me sleeveless isn't flattering on me, I figure, why not be comfortable? At some point, it's like: Whatever I wear, I'm not going to look stick-thin, and there are way too many cute tops/dresses that just happen to be sans-sleeves (and I mean, WAAAAAY cuter than what's out there in my size with short sleeves), so I just want to wear clothes I like, regardless of my arms.
I do have other parts I regularly hide (my low-hanging flabby stomach!), so I doubt my large arms are as unappealing to everyone as my abdomen. And if so, they'll have to get over the trauma