Is there any setting in texture painting to change the behaviour of the Dyntopo so it will generate quad faces rather than triangle faces ?
Triangles define better areas than quads (details). That's internal. There is a function on object mode, though. Click your object. Enter edit mode. Select all your faces. Press spacebar (I assume you´re on 2.79) and search: Triangles to quads.
You can also use REMESH from the modifiers. You can also try decimate to reduce the "poly" count.
The question was about a setting in Texture paint to handle allowing Dyntopo to use quads so that the mesh could be painted on.
The simple answer is no, Dyntopo is a live tesselation depending on brush settings for topology detail in sculpt, and is part of Sculpt and not Texture paint.
To properly use texture Paint with a dyntopo sculpt, one needs to either make use of retopology manually or with an add-on to redraw the mesh as a quads and paint that, or use something like Instant Meshes program to generate the quad mesh object automatically, and then paint that. Once you have the quad mesh, you can unwrap and paint, and still make use of Multiresolution modifier to then sculpt more details in the same form.