This work requires constant, homogeneous and of a precise color temperature light. I think the flash here is the best answer. It will be placed facing the camera. To have a more or less constant illumination over the entire surface of the slide, I interpose between the flash and the support a polystyrene screen, extruded or not. If I were really rigorous, I would take an empty image and I would measure the exposure at different points of the obtained image.
The choice of color temperature can be discussed. Personally, I select that of the source, ie. the flash. But one could judge that it is better to take the color temperature of the slide and therefore select the automatic white balance. If you shoot in raw, the question doesn’t arise, since the white balance is done a posteriori.
Since the flash is not mounted on the camera, its synchronization becomes a problem. The simplest solution: the classic sync cord; but often the modern equipment, flash or camera, doesn’t have the proper plug. The solution is to buy one or two shoes, depending on the needs, to place one in the camera's flash support and the other under the flash shoe. If you have a dedicated sync cable, you can of course use it, but I think it's too expensive if it's only used for this. There are finally master / slave flashes or radio transmitter / receiver transmission systems, but again, these are very expensive for such an occasional use.
Male/male Spiral sync cord 1,5 m
Hama 6938 - 17,54 € (price 2016)
Flash sync hot shoe
9,90 € (price 2017)