Can you try it on another mirrorless or another adapter ?
Usually that produces a more defined flare circle. To rule it out, test the lens on film.Some older lenses have a rear element that reflects light back to the sensor.
Only cure is return or sell.
Central veiling flare is mostly a result of internal reflections inside the lens. Check whether it has lost any of its inside antireflective paint as far as you can see. Otherwise the black edge paint on the elements may have been damaged in an earlier repair. The nastiest possibilities would be balsam separation on a cemented element (does this lens have one?) or internal haze (which can be removed) or fungus.




It looks like somebody polished the inside of the mount as well.I took some photos using the phone with some nasty flash but I think it does the job of telling that the aperture blades are too shiny 🙁
1)
IMG_3367.jpg by Billy W, on Flickr
2)
IMG_3368.jpg by Billy W, on Flickr
3)
IMG_3375.jpg by Billy W, on Flickr
4)
IMG_3376.jpg by Billy W, on Flickr
I think from pics 3 & 4 can clearly see how shiny the aperture blades are and I think there are signs of what jaapv said before: black paint around the edges of the lens have gone.
When I shone the iPhone torch in from the front of the lens and me looking from the back of the lens, I could actually see some reflection of the aperture blades. I think this might be the cause of my veiling flare on my copy of this lens.
Can the blades be made matte in a CLA?
It is possible that if you were able to ask the people at Kern why the lens has shiny aperture blades, which cause flare when the lens is aimed against the light... that they'd reply 'Why would you ever shoot against the light?'
I have two FED lenses that are similar, one of which shows central flare like your Switar. I took a photo that shows the loss of black coating on the edge of the lens is most likely the cause. Flarey FED on left, comparatively good on right: