You should have cut it off right away. Only mature plants should be allowed to bloom. These are not house plants. They need very bright light. If not full sun all day then 16 hours under a good compact fluorescent like 80-105w or a couple HO T5s.
These plants can be found at most Lowes and some Walmart stores but it's a bit early in the season. There are many online vendors.

The flowers aren't all that exciting anyway. The tap water is not good. I would recommend giving it a good soaking with distilled, cut off the flower, and provide it with ample light. VFTs can be brought back from the brink of death but only under the right conditions.

The plant did in fact come from a Home Depot. But if I can't keep this one alive there's no point in letting my daughter spend another $5 when they do come back around. The blooms are quite average but it's always better to be able to say you accomplished a bloom on a certain plant, not almost. It has already been cut off. I flushed the pot with bottled water. I need to pick up distilled just for it. I typically used the ends of bottled water left by the children. It is purified and not enriched, got to be better than hard tap water. It's what I had been using but forgot and used the watering can last few times. I'm sure it was the bloom that was hurting more than the water.

What denotes a mature plant? Since there is only one species with many varieties, is size the indicator or something else? I know I need to go back and do more reading if I want this to be a plant that sticks with us. I've kept alive this long so it has a good chance I feel.

A mature plant would be one several years old and would be recognized as being larger than the ones typically offered for sale. Plants in stores are usually in their first year out of tissue culture.

Even bottled water can be problematic over the long term because it is not mineral free. You can water a VFT with tap water for a little while because the potting mix will soften the water to a point, but eventually it will kill the plant. You can save a lot of money on distilled water if the pot is placed in a container to reduce evaporation.

Good luck with getting your plant to perk up. Once you get the conditions right they will often begin to multiply.

That is why I said I need to read up. The wife had gone through the FAQs when we got the plant but I'm the gardener so I guess I need to learn the finer points. I knew they could stand quite a bit of water. As for "in a container" are you meaning like a cloak? I knew it came with a dome, If I need to fashion something it is still small enough to do that. And for multiplying that is what I was hoping for but figured I should find that instead of ask. I grow bananas so I have been spoiled by plants that offset. If this is the way VFT grows then that is also a good indicator of general health.

Any type of clear container will do. The simplest I've used are the containers that grocery stores sell fruit in and they work fine. It can be completely closed if the environment isn't too hot, otherwise an opening in the top is needed to allow excess heat to escape.

VFTs grow from a small white 'bulb' that will produce little offsets but the process is pretty slow. You might get 1-3 smaller ones a year from a mature plant.

Don't enclose your plant. It doesn't need high humidity and it needs full sun which would make soup out of it in a container. Save rain water to water it with. I would rinse the media but let it drain some. Sick plants don't do well being soaked. Just keep the soil moist until it perks up then you can keep the media fairly wet by using a tray under the pot with water in it.