Does DaVinci Resolve work on Linux?
Yes. Blackmagic Design publishes an official Linux version of DaVinci Resolve.
The free version on Linux does not decode H.264/H.265 video; convert footage or use the paid Studio version.
How to install DaVinci Resolve on Linux
Blackmagic Design provides an official Linux version on its website.
Sources
DaVinci Resolve on Linux: common questions
Does DaVinci Resolve work on Linux?
Yes. Blackmagic Design publishes an official Linux version of DaVinci Resolve.
How do I install DaVinci Resolve on Ubuntu?
Download the Linux version from Blackmagic Design’s website: https://www.blackmagicdesign.com/products/davinciresolve.