I think that a genetic factor in regional accents would be extremely rare if not nil. Look at all the examples of people of different ancestry raised in other places that have no trace of the accent of their native land. People of Chinese extraction born and raised in the US or Canada have no hint of an Oriental accent unless their Grandmothers raised them. Urban African-Americans have distinctive accents which are easily identified is coming from the US. Yet raise that same person in Britain, and they'll have as thick an English accent as a person whose family has lived there for hundreds of years.
Vince, in general, I agree with you. However, you are still coming very close to making overstepping generalizations. What if there is a gene that affects one's ability to retroflex their tongue? In Japan, no one would notice -- Japanese doesn't use a retroflexed "r", but rather the combined "r-l" (like the rolled Spanish "r"). If we take a Japanese family with this and have their offspring grow up in the US, we would notice that they still can't pronounce the retroflexed r. And because we haven't transplanted every Japanese person and forced their kids to learn American English as their primary language, how can we take this absence of evidence to necessarily prove that there is no gene that affects retroflex? (Particularly since we've found that the ability to roll your tongue is at least partly genetic?) (Not roll as in Spanish roll!)
Essentially, all I'm saying is that genetic stuff is too unpredictable.
As a final note, you mentioned:
Genetic changes in humans don't happen very fast. It takes many generations of any significant changes to occur.
I always find it interesting that people express the power of genetics (if you will) in terms of "change". If anything, I would say genetics' abilities come from "numbers". It's because bacteria are so populous that we have problems with antibiotic resistance, not from their ability to "change". Lucky genetics has more to do with a particular bacterium's survival than its so-called ability to adapt, and luck requires high numbers for the low probability to result in success.
(Not that this is important in any significant way. Particularly for our discussion.)
(As a final final note, I loved your phrase "of Chinese extraction". Such wonderful imagery I see.)