I would normally highly advise against this idea, buy then I would be a hypocrite...
Rich is correct, a flashing red light on your vehicle (even in the rear) is illegal, regardless of who you are, unless it is a factory brake light blinker combo light some vehicles have.
Just be forewarned, that activating the "flashing" feature of these lights would be a very bad idea unless you are in a clearly designated OHV area. It will be tempting, trust me, but dont do it.
Now, to complete your wiring....
You wil first need to locate a pair of these:
except with the amber/red leds combined and with a clear lens. A colored lens will only be available if the leds are only 1 color. This will be a hardest step. IF you can locate them, you then need to purchase this:
you will have 2 switches inside the cab. 1 that turns the flasher on/off, and the other a momentary switch that selects flash pattern. This will be wired to the amber portion of the light.
then your brake lights can be wired to the red portion of the lights. I wouldnt use them as signals, because you cant use dual intensity lighting to distinguish between signal and brake.
All of this is IF you find the dual color lights, which will be difficult to find. If you choose to run 2 solid red lights, I can make a diagram so that you can use them as your flasher (dust lights) as well as a brake which will override the flasher at anytime and make the lights solid when the brakes are depressed. This will work with or without the switch turned on. That will require the flasher box shown above, plus 2 standard 5-pin automotive relays. If you really wanted to do signals as well, its possible. That would require 2 more relays for a total of 4. Problem with this is again no dual intensity for signal vs brake which is bad, and also red lights for "dust" lighting is not typical, ideal, standard, nor desired.
Your last option, which is the one I highly recommend, is go ahead and get the oval leds like shown above that you wanted, but just stay with 2 solid amber lights. No need for red at all! Unless you have glass bedsides and its caged with LT and you have no OEM tail lights, then sure, go ahead and add red lights to make it legal. Other than that, no need for red. The main purpose of these is going to be dust lights anyways, right?
I dont see a need to add any additional brake lighting. The LEDs tails are already pretty darn bright as it is.
One last option is if you had a lightbar like mine that has 6 amber lights in the middle, and the outer 2 are red, then you can disable the red lights from the flash pattern, as use them as brake lights instead, or just add the brake light override on just those 2 red lights. This is something I have been wanting to do with mine, just havent gotten around to it. However, that bar is about $200 shipped, plus you'll need a bar to mount it too since its too big to but on the rail of the bed. And besides, I dont want you to copy my lights cuz im the only one who has that setup (as far as i know atleast).
You decide what you want, let me know, i can either assist you by offering a wiring diagram for you if you know how to wire and how relays work, or if your close enough, I can offer install services for a nominal fee
Just decide how you want it, and we can go from there.
EDIT: I just searched for like 15 minutes and could not find a single dual color light in the style you want. They have:
amber w/ clear lens
amber w/ amber lens
red w/ clear lens
red w/ red lens
but not amber/red w/ clear lens. Your not going to find that.
You could always do something similar to this, but maybe rearrange the colors slightly different or have 4 lights. Maybe the center red and outsides amber. The possibilities are endless. The wiring is the easy part. Its just deciding how you want it to look.
or do something light this route: