There is a slight condradiction between a Lux I or III and flood beams, at least without using optics or diffusion lenses. Usually when people want a flood they stick with clustered/arrayed LED lights. They don't throw very far, but they give a nice, even flood. The problem with clustered LED lights is that the majority tend to be low quality and not worthwhile. The cheap ones seem to simply cram as many LEDs as they can into a given space, use minimal (if any) circuitry to provide regulation, and don't have good runtime. The common 3xAAA ones are the worst.
There are still good ones of course. The LRI Photon Proton is a nice 1AA one with supprising brightness. Better still it's dimmable so you can use a lower amount of light to conserve batteries. Runs well on NiMH rechargables.
The Inova X5 is a classic flashlight. Pretty inovative at the time too. Before then LED lights weren't much to speak of, but Inova put 5 in the head and powered it with CR123A batteries, which was somewhat unheard of in a flashlight apart from high-intensity xenon flashlights like Surefires. An updated version is available (brighter LEDs), and you can pick them up at Target. Unfortunately rechargables aren't an easy option. Reportedly you can use a 14760 li-ion cell (17670 is too fat), but you might have to add a spacer magnet to make contact, and you'll definitely want to wrap the cell in tape or paper or something to prevent it from rattling. Reduced output compared to using 2xCR123As, and I don't know how runtime is. Runtime with CR123As though is very long for such a flashlight, about 6 hours of peak brightness. Inovas are also practically indestructable.
One interesting option is the
Oval Light, a light designed specifically for walking. 4 LEDs (or a 1W Luxeon) project foreward, and 2 project down to your feet. Flashlightreviews did a
review and gave it 4 stars, which is good. Not the brightest light though. The 1W version is supposedly twice as bright, but I don't know if it's a flood beam or not.
For Lux I and Lux III options there's not many floody lights made by regular companies. However, there's a couple 5W lights that fall into the "flood" catagory. The tradeoff of course is that such a powerful light isn't going to have long runtime. There's the Surefire L4 and L2, and both can be had for under $150 (from lighthound or OpticsHQ, go to the Dealers forum and look at the Specials page), leaving money you can use to buy a rechargable battery kit. The L4 can use a 17670 and the L2 can use a 14760 lithium ion cell. However, neither light is the best choice to use at full blast for more than a few minutes. They get hot quick. Therefore I'd suggest the L2 for its low mode. Low on the L2 is rather enough to walk around at night and lasts a long time on the batteries. Plus you've got the high level (an impressively bright wall of light) when you need it. The Nuwai 301X-5 reportedly works well on Pila 168S/600S/17670 cells, albeit at a dimmer output than with 2xCR123As, but should still put out enough light for a nightime walk, with 2 hours or so of runtime.
The final option(s) you have is to take an existing light that doesn't have a flood beam and
give it a flood beam. There's a few ways to do this, depending on the light you want. If the light has a plastic lens, you could lightly sand it with some high grit sandpaper which will diffuse the beam into a flood. If the lens is easily replacable, you might be able to get a LDF (light diffusion film) lens from
flashlightlens which also works great. Or, just put some Scotch tape over the lens. The final option would be to get a flashlight that a Surefire Beamshaper fits over. A Surefire E2L with a F04 Beamshaper works nicely (plus you can pop it off and have throw if you wish). The E2L works great with 17670 rechargables.
Along those same lines, there's quite a lot of options for modifying/upgrading a plain old Minimag (many of which are far better than the Maglite's own MagLED lights), and very easy to do (most are simple drop-ins). Look
here for a rundown of them. Plus LDF lenses are made for Minimags so you can flood them up even more if you need to (a 3 or 4 cluster drop-in is probably floody enough, but with a 1W drop-in you might want an LDF).