A contingent fee is a fee based on a percentage of what you “win” in a claim. Physicians and psychologists are not able to charge in this manner as it is not ethical for them to. You can see that both the American Medical Association and the American Psychological Association have come out against physicians and psychologists charging “contingent” fees. This type of fee is relatively common for attorneys, as attorneys are expected to be partisan. However, health care professionals you hire for your claim are more like an expert witness and their opinions should not be viewed as unduly influenced or purchased by the highest bidder. Attorneys also have strict rules on what and how they can charge (ex: see https://www.vetadvocates.org/cpages/fees-which-may-be-charged-by-agent-attorney.
I’d be careful of any doctor or organization that wants to take a percentage of your VA claim pay; they may not be acting ethically or consistent with the strict rules that attorneys have to work under. Some of these organizations of course are neither doctors or attorneys. They may be paying a fixed fee to the doctor(s) they consult with and then charging you more. There are doctors out there willing to work with you directly in an ethical manner with fixed fees that you are aware of up front.