Black Cat and bad dandruff

[SodaStreamy]

We have a rescue cat (about 8) and whilst she wont sit on anybody for a cuddle she gets really happy when she is being brushed.

The problem is the slightest brush/comb and she is covered in white flakes.

She doesn't let us put a small bit of oil (as vet recommended) on her.

Any suggestions?
Will it be irritating her at all?

If she lets you brush her then can't you put the oil on the brush. Can't you stroke her? As surely then you could just put the oil on your hands and stroke her. I doubt it is bothering her if she doesn't seem to be showing any signs of itching, but I would mention it again to the vet next time you're there.