How would you go about doing this if it was a beer you are brewing
I brew all grain, just double the ingredients and tweak some.
But if I had to convert that Brewgr recipe to partial mash/extract, double all ingredients to brew 6 gallons.
1. If you can't source oat malt
and have it milled appropriately (very narrow gap) it should look like fine grits, substitute with flaked oats. Quaker or generic store brand "Old Fashioned," "Quick Oats," or "Instant Oats" from the grocery store is fine. They can be used whole, don't need to be milled.
2a. When substituting flaked oats for oat malt:
Mini-mash 4 pounds of flaked oats PLUS equal amount (4 pounds) of (milled) 2-row in 12-16 quarts (3-4 gallons) of water at 154F for 1 hour.
Lauter, sparge 2x. It's gonna be sticky, stir well and be patient. Lauter, then batch sparge 2x.
2.b When using 2 pounds of oat malt and 2 pounds of flaked oats, only add 2 pounds of (milled) 2-row to the 4 pounds of oats, and mash with 9-12 quarts (2.5-3 gallons) of water.
3. Adjust the amount of extract needed. This depends on how much grain you used in the mini-mash and the gravity and volume of the resulting wort (how many points of gravity collected).
4. Largely depending on size of kettle, heating source, and chilling method:
Add more water and some of the extract, or add later.
Boil that for 60'.
Add boil hops per schedule (until you get to your whirlpool hops)
5a. If doing a full volume boil, add the rest of extract at flameout.
Chill to the whirlpool temp, and add the whirlpool hops.
Chill and transfer to your fermenter.
5b. If doing a partial boil, leave the balance of the extract for later.
Chill to the whirlpool temp, and add the whirlpool hops.
Chill and transfer to fermenter.
Heat enough water to dissolve the balance of the extract, keep at 150F for 10' to pasteurize.
Chill and add to fermenter.
Top up with water to your recipe's volume (6 gallons).
I hope I covered all the principles...