Do you mean that I keep the two flashes in place for the actual painting, and use the card to reflect some of the light onto the gold towards the lens? Could I use a mirror or some other reflective surface?
Could it even be an idea to use an ordinary table lamp? Or what could I buy for this purpose?
I'm using two Lencarta Smartflash with soft boxes (in case that wasn't clear).
Most photographic lighting problems are complex, and the best answers often start with "it depends" and end with "and then experiment".
No photographer, however knowledgeable or skilled, can usually know exactly what lighting is required until s/he sets it up, but with this knowledge and experience, it's easy to know what CANNOT work, which saves time.
But this one is simple, because the subject is flat and two-dimensional and so the result cannot be affected by camera angle. Your solution was clearly identified in posts 2 and 4. light must always reflect at the same angle (the angle of reflectance = the angle of incidence) and, with the light coming from 45 degrees, it must reflect at 45 degrees, which means that the light reflected from the gold leaf cannot reach the lens and so cannot show the gold leaf in your photo.
So, as already explained, what you need to do is to have a third flash pointing straight on (90 degrees or thereabouts) to the surface, so that the light from the gold leaf is reflected straight back to the lens. Simple.
Reflective cards can help with a lot of lighting challenges, but not this one - think about it, for a reflector to work, it needs to pick up "spare" light and change its direction. In this case, it will be impossible to pick up this spare light, and even if this was physically possible, the reflector would need to be placed in front of the lens, which means that you'd get a photo of the reflector, not the painting!
In theory, a table lamp may do the job, but it would be physically far too large and because of its size it would need to be behind the camera, so would cast a shadow of the camera on to the painting - and the light colour would be wrong too.
So, back to basics - a hotshoe flash plugged into your camera and set at low power (experiment with the power) is your best answer, and my alternative of taking one shot with your two 45-degree lights and one shot with one 90-degree light and merging them together in post processing will give the same result with more work. Therefore, if you have just one painting to photograph, take two shots and merge them, and if you have a hundred to do then use a third flash.
Does this help?