Oneworld or not has got very little to do with it. The questions are first, whether you have one ticket or two; and second, what Silkair's policy is for through-checking bags.

If you have one ticket, you've got a pretty good chance that the bags will be checked through. Silkair and BA have an interline baggage agreement, so if you have a through ticket then you would normally expect through-checking to be a contractual entitlement.

If you have two separate tickets, you're then at Silkair's mercy as to whether its policies will allow through-checking. If you do this, you must make sure that you give BA your bag tag numbers in good time, otherwise there will be a good chance that your bags will not be loaded onto the BA flight. (Even if you're on one ticket, this is a good idea.)