Bower digital flash sfd290 cord won't connect to my canon rebel eos t3i

You need a PC sync socket on the camera. PC stands for Proctor Compur and this meaning of PC goes way back to the days of cameras with bellows and the photographer under a black blanket.

You can buy an adapter:
http://www.bhphotovideo.com/c/search?Ns=p_PRICE_2%7c0&c...
But from reading reviews, you may not be happy with this flash unless you use your camera in manual mode. I hate when people answer questions by suggesting the poster buy something else, so notice I did answer the question first by mentioning the adapter.

For a less expensive flash option that will work right on your camera and be truly automatic, consider a used Canon 420EX from Ebay for about $100.

If you intend to go into photography in a creative way, (more than point and shoot) sell the Rebel and get a used Canon 40D or 50D ($200 to $300) so you don't come up short on features like the missing PC sync port and other things you won't know about until you need them. With the Rebel you'll keep finding other limitations. With the used cameras I mentioned, they'll work great, have lots of features and control, and won't depreciate much (because they already have) so you can upgrade every year or two by adding just $100 to the sell value. That's how I went from a 10D camera up to a 1D pro camera over a five year period.

Finally here is a "positive" review I found of the Bower flash, notice the caveats:

"Had this flash for a Sony and now for my Nikon D300. I also have a SB-600 flash unit which is of course way better, but also way expensive - I guess nobody here should expect the same quality for 1/4 of the price.
The build is overall cheap but okay for the price, it will last a while when you take care of it. The major downside is that it's not really a TTL flash. The title says something about "automatic", I'm really unsure what they mean with that. Fact is, it produces a strong flash, you can swivel the head (even at the wall behind you) but it doesn't communicate with the camera. You can still use it on-camera though, but it's more like a manual flash gun, so operating the camera in auto-mode will most likely produce an overexposed photo. If you're unsure if you should buy it... it's an okay budget flash which will give you more options than the popup-flash, but if you're more like the I-use-my-SLR-only-in-auto-mode guy than better invest $100+ in a TTL flash which will get more information from and to the camera than: Fire flash now!

But here's the deal: Buy a remote FM-trigger (I use the "CowboyStudio NPT-04 4 Channel Wireless Hot Shoe Flash Trigger Receiver for Canon EOS, Nikon, Olympus & Pentax Flashes Other products by cowboystudio") and use this flash as an off-camera remote unit. Again, manual mode operation of your camera is recommended, but you can achieve great results with this off-camera set for $70 (flash + trigger). Combine it with a lighting stand, camera bracket and umbrella, and you have a portable studio lighting set for about $100-$130. This flash does even fit better on the remote trigger than my SB-600 because it has a screw-ring (not shown in the product picture) to tighten it to the flash-shoe-mount."