Before we start doing damage calculations, we need to make an artificial Infernape with every detail just like yours.
This is how our artificial Infernape looks. I have adjusted the EVs and IVs in such a way that they're not the same as yours (since yours are unknown and hence can't be replicated) but the final effective stats are the same as your Infernape.
These effective stats are ultimately what matter in damage calculation.
We will consider your Infernape to be level 73 for simplicity's sake even though you mentioned it gains a level mid-battle. This would give slightly lower odds, but that difference wouldn't matter much.
Calculation of Individual Odds
1. Spiritomb cannot get a critical hit with Psychic.
- Affection does not exist in Gen IV
- Spiritomb doesn't use any critical hit ratio boosting move
- Psychic is not a move with a high critical-hit-ratio
The chance of landing a critical hit is straight up 1/16. Hence, the chance of Spiritomb not landing a critical hit is 15/16.
2. I must flinch Milotic with Rock Slide.
Rock Slide inflicts damage and has a 30% chance of causing each target to flinch.
The chance of flinching Milotic with Rock Slide is 3/10.
3. Togekiss has to be sent out next. I have to either get a critical hit with Rock Slide (with Razor Claw odds) or flinch it with Rock Slide.
Since we need to know "how long you'll need to suffer," we'll go with the worst possible odds out of the two, which is a critical hit with Rock Slide.
The odds for a critical hit with Rock Slide holding a Razor Claw are 1/8.
4. Close Combat has to critical hit and OHKO Garchomp.
This is where uncertainties start to appear. The EVs of Cynthia's Pokemon have never been officially confirmed. Bulbapedia only states information about their IVs:
In Pokémon Diamond, Pearl, and Platinum all of Cynthia's Pokémon have 31 IVs in all 6 of their stats.
For the sake of making these calculations possible, we have assumed the information on this spreadsheet from this website to be correct.
Hence, all of Cynthia's Pokemon have 0 EVs in all stats.
Lvl 73 0 Atk Infernape Close Combat vs. Lvl 62 0 HP / 0 Def Garchomp on a critical hit: 211-249 (93.7 - 110.6%) -- 62.5% chance to OHKO
Hence, the odds are 62.5/100 or 625/1000.
5. Roserade must be OHKOed by Flamethrower.
Lvl 73 72 SpA Infernape Flamethrower vs. Lvl 58 0 HP / 0 SpD Roserade: 204-240 (131.6 - 154.8%) -- guaranteed OHKO
Hence, the odds are 1.
6. Lucario cannot get a critical hit with ExtremeSpeed, and I must OHKO with Close Combat.
- Affection does not exist in Gen IV
- Lucario doesn't use any critical hit ratio boosting move
- Extreme Speed is not a move with a high critical-hit-ratio
The chance of Lucario not landing a critical hit is 15/16.
Lvl 73 0 Atk Infernape Close Combat vs. Lvl 60 0 HP / 0 Def Lucario: 278-330 (161.6 - 191.8%) -- guaranteed OHKO
Hence, the odds are 15/16.
7. I can't miss a single Rock Slide on any turn.
You'll need to hit a total of 3 Rock Slide (see below - 2 on Togekiss and 1 on Milotic).
A : Hitting 2 Rock Slide on Togekiss ; P(A)=81/100
B : Hitting 1 Rock Silde on Milotic ; P(B)=9/10
P(AnB), i.e., the probably of both happening simultaneously is P(A)*P(B)=729/100.
Hence, the odds are 729/1000.
8. I can't get a damage roll that puts a Pokemon into Full Restore range.
To calculate this, we would have to assume this answer to be correct. So we need to avoid getting a Pokemon below 25% HP.
Lvl 73 72 SpA Infernape Flamethrower vs. Lvl 58 0 HP / 0 SpD Spiritomb: 99-117 (69.2 - 81.8%) -- guaranteed 2HKO
The chance of avoiding the 25% or below HP range is 46.03%, or 4603/10000. (You'd actually want a low-roll here)
Roserade: It goes down to a single Flamethrower. The chance is 100%.
Togekiss: Although Close Combat does more damage, I have used Stone Edge for calcs to prevent defense drops and because we want lowest possible odds.
Lvl 73 0 Atk Infernape Rock Slide vs. Lvl 60 0 HP / 0 Def Togekiss: 90-108 (47.3 - 56.8%) -- 87.5% chance to 2HKO
The chance is 87.5%, or 875/1000.
Lucario: It goes down to a single Close Combat. The chance is 100%.
Milotic: It goes down to Rock Slide + Grass Knot without Rock Slide putting in the <25% HP range. The chance is 100%.
Garchomp: It goes down to a crit Close Combat. The chance of OHKOing with a crit and avoiding the <25% HP range is 1/8.
Hence, the combined odds are 503453125/10000000000. (That's 5.03453125%)
Have fun lol.
Help this helps! :)
Don't ask me how much time it took me to make this answer.
Special thanks to Pokemon Showdown! Damage Calculator and Pokemon Showdown! Teambuilder for making these calculations possible.