How much experience is required to apply to be on the editorial board of a journal
I believe this will depend partly on the field, and heavily on the journal. Is this a prestigious journal? Is it an area specific journal? In my own field, however, you can often email the editor (for smaller journals specific to your own specific area) if you've published a few articles with that journal, and they ask you regularly (say, 3-4 times a year) to review an article for them. In those cases, they will sometimes be happy to add you to the editorial board if you ask. Obviously, more prestigious journals will have steeper requirements, but if you're an early career academic, you should probably start off with a smaller, area specific, journal.

In this specific case, it can't hurt to apply. But if it's a prestigious journal in your field, I wouldn't keep your hopes up. If it's a smaller journal in your field, ask yourself if you want them to send you every paper with odd-ball stats that you need to review. Is it worth it in that case? It's helpful to everyone to be on an editorial board, so be sure to ask yourself why they have to put out an open call to find a board member. It may be because it's a smaller journal and there are no experts in the field, or it may be something else. You'd be the best judge of that question.