Yes, Amazon's referral fee is a percentage of the product price, so if the price goes up, the fee goes up. However, some product categories have higher referral fees than others so it is always good to know what percentage will be charged on the products you are selling.
Below is a link that lists the referral fees for each category.
https://sellercentral.amazon.com/gp/help/external/200336920
Also keep in mind there is an applicable minimum referral fee that is charged to sellers if the referral fee percentage comes out lower. In other words, if the applicable minimum referral fee is $0.30 and a referral fee percentage of 20% of the sales price comes out to $0.15, then Amazon will charge the seller the minimum fee of $0.30 since it is the higher of the two.
How much in fees does Amazon charge me?
Why are Amazon's fees increasing?
Why is Amazon taking more money from me?
Are seller fees a set amount?