Alright, a couple things I have to take note about this. First of all, should you make a webcomic? YES. A better question is why you wouldn't. ESPECIALLY if you want to practice your art.
Look if being a comic artist / animator is what you want to do as a career then you better start practicing as soon as you can. And a fanfic comic series would be a good way to get started practicing - given you hold yourself to some strict guidelines. What do I mean by this? Well, let's assume that you become a paid comic artist - I'm not going to lie, I know virtually nothing about the industry, however I can guarantee you there will be deadlines for your work. A good way to prepare for these harsh deadlines would be to start a comic web series and set a realistic deadline for every chapter and stick with it. If you say that you're going to release a chapter every week, release a chapter every week. It will be hard, but you need consistency with your deadlines otherwise you will never learn proper pacing.
Alright, enough of that. My next topic point: money. You already kinda answered your own question, but if you use the DC characters you cannot ever make money from it. Unless of course you work for DC. Ok, so you want to make money for your work. Who wouldn't? But how would you make money, you may be wondering. Well first of all, you'd need to use your own characters. Nothing DC [or other companies work] can be called your own if you plan on making any money from it. Lets assume you are creating an animated web series [your own story/characters], you can upload your series on youtube and over time you will [hopefully] gain an audience and then income. I could explain in extreme detail on exactly how you'd make money on youtube, but as it Is Im typing a lot - if you wanna know more just ask and I can explain in a separate reply. Alright, so thats how you make money from an animation, but what about a webcomic? Well admittedly I know less about that, but its roughly the same idea. Upload your webcomic to a website that you own, add advertisements to your website, and overtime you'll make money off of the advertisements on your website.
Ok. Next point; getting noticed / getting your work flagged. If you take everything I said above to heart, you'll never have to worry about getting noticed in the wrong way, and having your work flagged/removed. The only times this will happen is if you try to profit off of someone else's work. Thats a big no-no. IF you choose to make a DC webcomic, you MUST make it very clear that you are not and will never make any profit off of that work, that it is a fanfic - and even then there is still a chance that you're work might be removed. Copyright is a very tricky thing, but most of the time companies don't hunt down copyright violators unless they're making some serious money from the companies work. I want to be clear here, just because you use someone else's character without any profit does not mean you aren't violating the copyright. It just means that there is a very high chance that nothing negative will happen.
Now for my final bit here. I may have started to discourage you with everything I had to say. In today's age, everyone is trying to compete with everyone else. If you are feeling doubt about if you really want this or not, you need to draw a line in the sand right now. If you pursue a career in animation/comics, you need to keep at it. Consistency. Without consistency, no one will take you seriously. Set realistic deadlines for your work - once a week, once a month, twice a month, whatever. Just whatever you say you're going to do, be sure to do it. I wouldn't bother trying to start both animation AND a webcomic at the same time - unless you really have nailed down your time management skills. I've done some animation in the past - it takes A LOT OF TIME. Hours upon hours of work for maybe half of a minute of animation. I've also been working on a webcomic of my own for a few years now, and I can tell you that a webcomic also takes A LOT OF TIME.
Should you start a fan comic? I don't know. It depends on what kind of audience you hope to attract. The benefits of a fan comic is you'll be bringing in an audience that loves the same characters that you are drawing - as oppose to starting with your own story, in which you'll have to attract an audience from nothing. If you do start a FAN comic, you'll need to be careful but consistent. It may not be the worst thing in the world to make a fan comic, and then transition your audience to your own work.
Regardless of what you do, you should absolutely do something. And again, be consistent with your work.