Joint Skyteam lounge in HKG no longer exists -- https://www.skyteam.com/en/lounges/

As noted above, access to Centurion lounges with DL Reserve is limited to those flying Delta-marketed or Delta-operated flights (the same rules apply to DL Sky Club access). Generally speaking, if you purchase off the delta.com website, partner flights will be DL marketed (and will show as such in e-Receipts). If purchasing elsewhere, buyer beware.

https://www.americanexpress.com/us/c...card/38133-9-0
"U.S. Basic and Additional Delta SkyMiles® Reserve or Reserve Business American Express Card Members receive complimentary access to The Centurion® Lounge when flying on a same-day Delta-marketed or Delta-operated flight. "

Also, STE+ members (including DL) flying KE operated flights should have access to Plaza Premium lounges at HKG according to Skyteam lounge finder (unlike DL, they still provide lounge access to third party lounges when flying coach).