Oh wow, afraid this is a a long story... skip to the bottom if you just want a short summary.

I found out I was moving, and promptly decided that I was going to dye my hair blue. It was already a dark purple, but blue sounded like more fun. I didn't really think about it, and let my friend do it for me. After bleaching it once(without telling my parents), it was a lovely shade of orange-purple-yellow-brown-hot pink. After a second bleaching (the same day, I know that was one of the STUPIDEST things I've ever done) it was honestly about the same. Thankfully, it didn't fall out, become gooey, or do anything besides what a TON of conditioner can cure. My hair was pretty long, and my friend had NO IDEA what she was doing.
The next morning, we tried dyeing it blue anyway, even though it was about 10 different colors already. Initially, my hair was a shockingly even shade of nearly black blue. But, as soon as the black started fading, it suddenly became about 20 different colors.
I knew I needed professional help with my hair at that point, but the only thing I could get any hairstylist to do for less than $175 was dye the whole thing pitch black. So that's what I got. My hair was dyed with a semi-permanent dye that left it black with a blueish tinge.
I was lucky, my hair was still in pretty good shape, daily conditioning was all it really needed.
Not too long ago, my roots were really growing in, and I wanted a new cut as well. So I got my hair in the back cut to about 2 1/2 in. All my blond roots (which was the entire back of my head) were dyed a natural brownish red color, and my entire head given a red tinge. The previous blue tinge had faded out, and the new colors made my head blend together a lot better. The front of my hair is a few inches past my chin, and right now as the brand new roots, un-dyed and blond, the natural brownish red shade, and the super dark brown/black area at the tips.

SHORT VERSION:
1. Dyed hair purple with permanent dye (no clue if it was metallic or not)
2. Bleached it TWICE in one day two weeks later (NOT a solid color afterwards, some parts still purple, some orange, some yellow, some white)
3. Dyed it semi-permanent blue the next day (black first, but faded awfully)
4. Got the whole thing professionally dyed semi-permanent blueish black a week later
5. Left it alone for a 3 months or so
6. Got most of it chopped off in the back a month so so ago, got my blond roots dyed red-brown and the rest dyed a more natural super dark brown to help blend the whole thing together

SO! Now what I want to do is put BRIGHT RED (not "natural red", closer to a firetruck) streaks in the front of my hair, and just dye the back the same color.
All the hair on the back of my head is short (I spike it) and WAS NOT part of the whole dyeing/bleaching fiasco, it's only been dyed the reddish brown.
However, where I want the streaks in the front IS three different colors (about a 1/2 in of my natural blond roots, 2 in of red and 7 in of black.)
Would I be able to get it the bright red I want in the front (without going to a professional)?
Is it safe for me to bleach and dye the back?
I really just have NO CLUE how I would go about getting the color I want, besides just waiting until it all grows out. My hair is pretty resilient, while it was really dry after all the bleaching, it feels completely healthy now, only problem I have is it getting too greasy (same problem I had before all that I did to it).
Still, I don't want to end up with the zillion ugly colored hair I had before.
ANY help would make me extremely happy!

Your hair has been through a lot so I wouldn't try to put it through too much more. Red is a fairly easy colour to achieve because your hair doesn't need to be pale blond for it to work.
I would play around with a few strand tests. Check the condition. Check how much you need to bleach it before you can get the colour you want. Test the bleaching and colouring on the various shades of your hair. It's the only way to find out if it's going to work out.