I am thinking about learning boxing for punching, TKD for kicking, and wing chun for flashy moves, jabs including eye jabs, and center line theory.
Will that be effective?
First, review my answers at the following links:
Those links go over the same material that I'd just be reiterating here. So please review them first before moving on.
As for Wing Chun and Taekwondo in particular, both styles are, in my opinion, different enough that combining them will cause only minor confusion. And ostensibly, they both complement each other. Wing Chun closes a hole that Taekwondo has in the close range. And Taekwondo allows you to fight at a distance that Wing Chun isn't good at.
The main problem you're going to face is that you can't integrate them very well, since they have very different stances and methods of power generation. Moving from a Taekwondo stance to a Wing Chun stance and back will be difficult, involving a lot of moving parts. That will waste time and will make you vulnerable to getting hit in between.
You might consider keeping both styles more or less separate in your new combined style. You would then only switch to Wing Chun when the range was closed (either by you or by your opponent). You would use Taekwondo only when the range was far apart. That leaves transitioning from one to the next as your biggest challenge and probably the weakest link.
Consider that in most branches of Wing Chun, you are leaning back slightly. In Taekwondo, you are upright. So to move from one to the other, you have a lot of motion you need to do with your spine, which causes you to have to reconfigure your shoulders, hips, and knees. It can be done, but it does create a lot of motion, which could make your movement less efficient and therefore sub-optimal.
If you're fine with that, no problem.
Otherwise, what you might try doing is seeing how other styles have handled this. Muay Thai, for example, has an effective answer in the close range, the kicking range, and everything between. They do not change their stance or methods of power generation in transitioning from one range to the other. There is consistency of movement throughout. Ask yourself if they've lost anything in order to gain that consistency. And then direct that insight into the task of integrating Wing Chun and Taekwondo.
As for effectiveness for self-defense, MMA is now considered kind of the gold standard for effective fighting. That's because of the way it is trained, not so much that its techniques are "better". They practice with "live" partners that are actively trying to resist and defeat their opponents. There's no compliance involved, your partner will keep going, and you don't know what's coming ahead of time. It's what is known as "pressure testing". Without that, the effectiveness of a martial art for fighting and self-defense is minimal.
Pressure testing that can only be done once isn't very useful to you. You need to be able to do it again and again, day after day. That means you can't keep getting injured. If you do, you will quickly quit and go do something else.
So that means you need some rules to prevent injuries. Once those rules are established, and the risk of injury is minimal, then you can train hard on the core techniques.
I talk about this more at my answers in the following links:
That understood, how does Wing Chun's eye jab come into play here? To answer that, ask yourself: Can it be pressure tested without injury? The answer is generally no.
But I would ask if the Wing Chun eye gouge is a core technique that deserves practicing. There have been UFC-like competitions where eye gouging was either allowed or was merely fined by a trivial amount of money. And yet, the traditional stylists found they were not able to deliver their eye gouges to fully resisting opponents. They simply lacked a set of core skills needed to be able to carry it out.
What I'm getting at is that eye gouging isn't a core skill. And, if you do have a core set of skills which allow you to be in a position to be able to use the eye gouge, you're probably going to find that a punch, an armbar, or a choke would be better in almost all situations. And those are techniques that you can practice and get good at, whereas the eye gouge isn't.
Eye gouges also put you at considerable risk for breaking fingers, because it's really hard to 1) target the eyes as your opponent's head is moving, and 2) use enough force that you don't hurt yourself. Even in Wing Chun, it is stressed that these are techniques of last resort, when everything goes wrong. They should be given nearly no practice time. You instinctively know how to do them already, just like you know how to bite. Biting isn't a core skill that you need to practice, either.
There are ways to do eye gouges without the risk to your own fingers, by the way. We've seen this in MMA competition. It's typically done by accident by pushing your palm out towards your opponent's face, keeping your fingers slightly bent. Here, you're not leading with locked, straight fingers pointing at your opponent's eyes. Instead, you're almost slapping very lightly. Even a light eye poke can blur your opponent's vision. This is done so often in MMA by accident that it effectively does cause people to become better at defending against it.
What I think I would take from Wing Chun more than anything else would be two things: 1) The offensive blast of chain punches, and 2) the basic concept of the chi-sao sticking hand technique. Wing Chun fighters do sometimes win against people who are not expecting someone to just keep punching right at their face. I've seen this many times before. They take the first two hits and back up, expecting their opponent to let them gather themselves. But instead, the Wing Chun stylist follows them and keeps punching at their face. It can be very frustrating to someone who has poor head defense and defensive mobility.
Whereas, the sensitivity that chi-sao gives you can be useful in a variety of ways. Mostly I wouldn't worry about the techniques themselves (bong-sao, lop-sao, etc.). The thing to take is the idea of connecting and being sensitive to your opponent's force when in grappling range. This concept can be used in fighting, but in my experience, it should only be used momentarily. You shouldn't go down the line of thinking that the goal is to remain connected. That's not the goal. The goal is to win the fight. The connection is just a momentary tool to get you further along in that goal.
But while we're talking about limitations of Wing Chun, Wing Chun has holes in its defense also. In particular it's susceptible to hook punches from boxing. It's better than nothing. But you might want to consider something like muay thai or boxing to deal with the short and mid ranges.
Remember when I talked about pressure testing, rules, and how the style itself will need to be modified if it performs sub-optimally given those rules? Wing Chun has no "rules" and no standard way of pressure testing the art safely and repeatedly. As such, it remains a conceptual / theoretical style, as do most kung-fu styles.
Some Wing Chun schools have some form of sparring. But it often ends up looking like sloppy boxing, not Wing Chun. Or if it does look like Wing Chun, it's usually because the teacher enforces adherence to Wing Chun principles for both fighters (they won't generally do sparring vs. non-Wing Chun people). It's not the same as pressure testing, because in pressure testing, you take your results and figure out what needs to change about the style. With Wing Chun, the style itself is taken as untouchable, so it must be the fault of the student that he/she wasn't able to make it work.
Anyway, I mention that, because if you're interested in adding Wing Chun to your fighting style, you need to understand that it is theoretical and may not work when pressure tested.
I talk about this to some degree in the following link:
My thoughts anyway.
Hope that helps.