To show Vertex Colors in Edit Mode, turn on "Attribute" color from the Viewport Shading menu.

If you are using Substance Painter, you can bake your ID map from the Vertex Colors in your imported model. Go to the Bake panel, choose ID, and then change Color Source to Vertex Color.

For other programs, you can alternatively bake your ID map from within Blender. To do so:

• Create a new material and assign it to all objects that share a UV map. 
• Go to the Shading panel and create this node setup:

• Click "New" on the image texture and choose your resolution, then click OK
• Ensure your Render Engine is set to Cycles
• Scroll down in "Render" properties to the Bake section.
• On "Bake Type", choose Emit
• Click Bake.
• Your baked ID map should now be in the Image Texture that's selected in the image texture node.