Actually BA codeshare to DPS through HKG. However, this involves an overnight stop at HKG on the outward, so I haven't yet seen ba.com or any booking engine offer it as a through connection.

IIRC, booking it in J results in a full J fare only of abour £5000.

As VC10Boy correctly noted, the best way is through SIN with a cheap QF flight (Tues and Sat only) onward.

If you go via HKG, you will find the add on fares for CX, HKG-DPS to be expensive. This is an expensive route. However, CX holidays offer the fares cheaply if combined with a hotel package.