That's a bit of an ask, but is doable in theory.
Win 8.1 can be used for the 15 beta.
Here's some instructions on the DLL.
As for the GTX 680, you'll see a rolling log
here - the 15 beta does recognize the board, but disables RED GPU decoding due to insufficient CUDA support.
If you're happy with Win8.1, you can go with that and try the 15beta out. You are likely to stumble on some limitations (lack of H264 encoding, IIRC), but the software can be ran. For full functionality, you'd need to upgrade to W10 - or to downgrade your W8.1 Resolve to 12.5.6.
The Linux port is slightly different in its ways, and CentOS is hardly the optimal platform, all things considered.
Linux Mint 19.3 | DaVinci Resolve Studio 17.1 | 2700x 32gb Radeon VII | macOS Mojave