I've successfully got Fldigi and DXLab Suite working nicely together using the Fldigi-DXLab Gateway. My TS-590S, Fldigi and Commander, DXView, etc. work just fine.
I made another configuration of Fldigi for my other rig, a TS-990. However, I'm at a loss as how to create a second Gateway configuration to launch Fldigi for the 990. Or is it possible that one Gateway configuration will allow you to select a specific Fldigi configuration?