Where to start...

• If you had connected the red (presumably hot) to the ground and turned on the breaker, the breaker should have tripped instantly. It's a dead short to ground.
• I'm hoping this is just a temporary connection because those splices need to be made in a junction box (secured in place) and use box connectors (plus a anti-short bushing if you use the FMC).
• The equipment ground coming out of the oven needs to connected the grounding conductor. If you use a metal junction box, that needs to be tied in as well.
• What's up with the flexible metal conduit, is there type NM-B cable inside of that? Typically one would use a insulated grounding wire when pulling wires in FMC.
• There's seems to be a disparity in the size of the wires (maybe it's just the picture). I'm guessing the oven requires a 40 amp circuit, which would mean a minimum of 8 ga. copper wire on the house side.
• It looks like you have NM-B cable coming out of the oven, I'm not sure if that's approved or you need to use actual cord.

I can't tell you why the oven isn't working. I'd think that connecting one of the hots to ground wouldn't impact the oven but I don't know.

I think you need to a get a licensed electrician in there to inspect your wiring and make the connections. With all due respect, I don't believe you are at all qualified to do this work.

The metal clad wire is the whip from the oven. Which is why the wire size is smaller, it usually is.

Yep, you need a box, metal perhaps, with the correct connector clamps for the metal and NM wire. The grounds should be connected, also to the box.

This is a 220v circuit and uses two breakers tied together. If you shorted the red to ground, the breaker should have tripped, though maybe just one side. Did you reset the breaker (turn fully off then back on)?

The microwave is on a separate circuit. Use that for the Hot Pocket.

And the fact that you don't know that the microwave and oven are on separate circuits is scary.

"I realized instantly as soon as it started to smoke"

1. WHAT started to smoke? That is, where did you see smoke coming from?

2. Did you by any chance connect the ground wire that goes to the oven to the red wire?

3. I'm puzzled about something. You matched colors for the R/B/W wires. Why didn't it occur to you to also connect bare ground to bare ground? Why on earth would you connect the bare with red? I'm curious about the thought process here.

4. I assume this is a temporary, see-if-it-works hookup, because what I see here sure isn't safe or code-compliant. A junction box isn't optional.

5. I see that you're a realtor. I hope you're doing this in your own home and not a client's. The law allows a homeowner to work on his own home's wiring (with a permit), but not on anyone else's home's wiring unless he or she is a licensed electrician.

6. Not that I mean to offend, but even if it's your home, I'm pretty concerned about the situation. Please get a knowledgeable licensed pro in there to do this installation safely.

Weedmeister,

If the FMC is the "whip" from the oven, why the bare copper wire? The only bare copper I've seen is #8 and larger and that doesn't look like #8. If it came from a piece of NM-B, I was under the impression that the insulated wires inside the NM-B are only approved when used as an cable, not individually. I'm just guessing but if the grounding wire came from a piece of NM-B, so did the rest of the wires.

If an undersized whip is approved, how much undersized? Then I'm wondering why cordsets for ovens are full sized conductors (except for the grounding conductor)?

Fixture wires have different sizing requirements than the branch circuit wiring. I'm pretty sure that oven only requires a 20A circuit (it's only 3400W, so a touch over 14A).

Realtors should not be touching wiring. It's illegal and the fact that you almost caused a fire is indicative of why. Chances are the breaker is still tripped but it's also possible you smoked some other part of the circuit (including either the oven itself or one of those hideously taped wirenut connections). Get your fingers out of this and call in a professional electrician.