Getting into new PhD after failing comps
Two bits of advice. 

First, your SoP should be as positive as possible without hiding the setback. Talk, as usual, about your goals and how your preparation makes you a likely success. 

But, I think more important, use your adviser's personal/professional contacts to help get you in the door somewhere. The advisor, even beyond a LoR, can boost your chances if they are willing to speak to others they know who can help you. 

If you say "I failed comps, but ..." it is an entirely different thing than a professor saying "He failed comps, but ...". The professor is putting their reputation on the line for you. It is likely to be respected.