A percentage is another word for a fraction. A fraction of 100 specifically. So to express 0 as a percentage of 0 we're asking the question: what is 0 divided by 0? This is an interesting question because there are four possible ways to answer it. In one sense we are taking an even number and dividing it by itself, making the answer 1 (100%). In another sense we are taking a zeroth of something, making the answer 0 (0%). In another sense, to divide by zero has an undefined solution, it's a quirk of mathematics that doesn't actually mean anything. Like if I said the words: Three plums diefy. That sentence follows all the grammatical rules of the English language and makes internally consistent sense. But it doesn't actually relate to anything in reality. Likewise 0/0 follows all the accepted grammatical rules of mathematics, but relates to nothing, so the answer is indefinable.
There is another fourth answer which Scientists tend to use. We tend to think of division by zero as being equal to an infinite solution. To put it crudely: dividing by 0 = infinity. There are definite examples where this can be shown to be the case, any inversely squared distance law gives the answer of infinity when dividing by zero, so Scientists think of it like that. However, Scientists also treat this as evidence that our hypothesis is wrong. If you divide by zero and generate an infinity, you've got something which can't be described in terms of the actual world, since nothing is truly infinite.
The best answer to the question is really to say that the question is grammatically sound but semantically meaningless. It doesn't actually make sense as a question and is, as such, unanswerable.