The welding rig goes in the “center” slot. To get it on your flatbed, you just need to remove whatever part is taking up this slot on the tile you want to install the welding rig on. Some examples of parts that use this slot are:
quarterpanels
trunks, boxes, etc.
seats
windshields
doors
Basically, anything that gets in your character’s way or is otherwise part of the “middle” of a vehicle is probably a “center” part. If you want a full list, just open vehicle_parts.json (it’s in your Cata folder under data/json) and look for the word “location”. It’ll show you every vehicle part in the game, and where it gets installed to.
Hope this helps, I’m glad people seem to get so much use out of the crafting stations, like the welding rig.