A known issue was recently added to the release notes, caused by the 1.3 game patch.
Fallout 4 - Flickering may be experienced at various game locations with the v1.3 game update and with AMD Crossfire™ enabled. A temporary workaround is to disable AMD Crossfire™
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We have just updated the Crimson 16.1.1 Hotfix driver to address the flickering experienced when Crossfire is enabled.
Please download the driver once again and reinstall it to fix the issue (remember to uninstall the existing driver first)
I'm running Crossfire with a 390X and 290. I moved over to the latest Fallout 4 Beta and it has been running well for me. You might consider giving it a try. The "Betas" option can be found under the Properties menu for the game in Steam.