I don't think BA will through check to a non-OW airline (as discussed in another thread), and as Dragon Air and China Eastern are not part of OW you may have to get the bags and re-tag. Still, worth taking your chances and hope that a nice check-in person will help you out, but remember they not obliged to do so.

Otherwise try to travel light and take on what you can in hand luggage (remembering to keep within the stated limits).

Getting around HKG airport is pretty easy so even if you are going between arrivals and departures, it will not take long. Even the with a re-check I think you will be done within 30-45 minutes maximum.