It's a combination of things, really...
Flashes are most likely to glare when taken straight on against the subject. It's the same principle as photographing yourself in a mirror with a flash.
Angling the flash, however, will reduce that... or changing your angle relative to the flash (same thing, really). With a built-in flash, shooting at a downward angle, for instance, might help... but you get that hideous distortion in the water that will hose the focus of your subject. Like I said, tank photography is not without its challenges.
My flash is a top-mount type speedlight - but I don't use it on the camera. In the hot-shoe where the flash would go is a wireless transmitter (model MT-E2). My flash can now be anywhere that it can see the infrared remote control beam (which can be tens or a hundred feet away and at shockingly odd angles sometimes since the infrared bounces like mad on anything reflective... try operating your TV remote perpendicular or even backwards sometimes if there is a shiny surface nearby).
This allows me to move the flash around freely. In some cases I shoot fairly straight, but I have the flash slightly above and to one side and I'm practically against the glass with the lens. This kind of scenario is making the frame so tight that the glare you describe isn't within the frame itself. In other cases the angle itself eliminates the glare.
You can, of course, end up creating scenarios here where you don't get glare but instead light the tank such that it ends up reflecting you.
I've got quite a few shots I'd like except that I can faintly see myself or my camera overlapping the subject or just off the side. Sometimes you can crop that out or remove it in Photoshop if you're so inclined.
The best shots, though, are coming from placing the flash overhead. This is an acrylic tank, so the top is mostly covered and provides a lot of flat, clear surface area. I can literally lay the flash down on the acrylic top and the receiver will get the infrared triggers through the water from where I am at eye level. The result is a light that comes down very much like sunlight and doesn't create harsh shadows. I tend to use a diffuser as well that scatters the light more.
Multiple flashes would be great and I'll try that someday when I get more speedlights. I can borrow some from friends with compatible models to try it out and have been meaning to do so for a while. This wireless transmitter also has the ability to do ratios. That means I can assign multiple flashes to two different groups and declare the ratio of light I want (more for A than B, for instance) while it remains proportional. That would allow for a strong light from the top and possibly a lesser light from a side (or behind) or vice-versa.
One thing I'll point out about Canon flash systems (and this is true for their Powershot series of cameras, too... so it's not limited to SLR): they are very, very intelligent. When you take a shot, the flash actually fires twice. The first shot samples the effect of the flash on the scene and the meter samples this combination of flash and available light. Based on the result, it adjusts the flash up or down and fires a second time to actually take the picture. This all happens so fast that it looks like one flash burst. You literally cannot see this happen since we're talking fractions of a second... you just hear the shutter and see a burst. This ability exists even in the wireless mode.
The more light you have in the scene, the less the flash has to produce. You can tell this both by eye and by how long it takes the flash to recharge. If I need a lot of light, I get a big flash and a longer recharge time before I can get another shot with the flash. If it's just filling, I can likely get quite a few flashes out of it in quick succession before it has to recharge. Since this camera can do 5 frames per second (the buffer rolls them out as new ones come in, so it can be continuous until the card fills up - sounds like a machine gun), rapid fill flashing is a real advantage. Fire off five shots, select the one that works... or end up with an action sequence that can be neat in its own right - like looking at still frames in a video. The flash in this case is kind of like a strobe light going off - flick flick flick flick flick.
If your flash is built-in and not movable, the glare situation is going to be hard to tackle. You might gain some benefit by diffusing the flash. You can do this by putting some kind of translucent or gauzy material in front of it. It might not eliminate it all, but it might be less harsh or less of a star-like burst in the frame.
Also, try getting very close to the glass and seeing how that affects the image. The more distance between you and the glass, the most opportunity you have to be illuminating the surface and not shooting through it.
Does your camera have a flash hot-shoe on the top? Many non-SLR digital cameras have these. If so, the door is open for an external flash like I'm describing. You can also get a slave flash that fires when it sees the internal flash go off. There are ways to rig it up so a transmitter can see the internal flash and send a signal to a slave flash while not exposing the internal flash to the scene. That will likely be far more trouble than it's worth - just depends on the design of the camera and your willingness to do bizarre and possibly counter-intuitive things.
Another thing to experiment with...make the room VERY dark and even leave the tank lights out. Set up a shot for a long exposure and use a cheap handheld flash or strobe manually. It's called painting with light and the results can be gorgeous. You might be able to borrow or score a totally manual older style strobe for super cheap. The camera will need to be on a tripod or resting on some surface. The cool thing, though, is that you can do an exposure of several seconds and flash multiple times... what ends up in the picture are the things it sees in those instants of brilliant light. This would also include some very neat shots where the same fish is several places in the tank in one picture.
In thinking about this, it also occurs to me that you might be able to pull off what I'm describing above using two cameras. Set one up for the long exposure and use the other to generate the flashes. This could be a digital and a non-digital with no film in it, for instance. All you're needing here is the source for the flash that can be moved to a different angle.
It's all about experimenting. The things that are challenges when taking a "normal" picture might be turned into ways to make some very, very creative images.
That's also the benefit of digital... unlimited "film" and no processing fees with instant feedback. Do really off the wall stuff and you'd be shocked what kind of neat results you can get.
Hope this is helpful (albeit long)...