How do people make fried onions as an ingredient as opposed to a snack? Should I coat them with flour, milk, and spices?

First - by your description of "fried onion" as a snack or appetizer and by seeying some videos on instagram I think the problem is in translation.

In polish "fried" onion would refer to one that are coated and deep fried. That look like flowers. Coating is a batter that is similar (or identical) to the one on onion rings.

But from the photo the name would in polish would be "roasted onion". Below is recipe I use (the only difference is I try to cut onion in little cubes while the asian make stripes).

4 onions
3 flat spoon of flour
1 flat teaspoon of salt
Pinch of sugar
Oil - quantity depending in what you will fry it, the idea is that when you add onion there shouldn't be an excess amount of oil.
Cut onion (in stripes or cubes), mix in bowl with two spoons of flour. Leave to rest while in fryin pan you heat the oil (the best would be just above "middle" on your settings). When the oil is heated add third spoon of flour mixed with salt to the onions. Put onions in oil (it should sizzle) and turn the heat to one quarter of your setting (beetwen "off" and "half"). Stirr the whole time until the temp go down. when the oil is "calmed" and slowly bubbling stir every minute. Fry for 20-40 minutes (depending on pan and heat) and until it get that golden brown color. Sif the onion and spread on paper towels to get ride of oil and sprinkle (while it's still warm) with pinch of sugar. Leave to dry.

You might want to look up recipes for "Bawang Goreng", which are Indonesian fried shallots, which should also work for onions. It's basically just thinly sliced shallots, deep fried until golden, and then drained.

You can buy containers of them at many international grocery stores.

If you're going to make them yourself, I would highly recommend purchasing a mandoline if you don't already have one. This allows you to slice the onions very thinly (needed to make sure they dry out fully before they burn), and a consistent thickness (so they all cook in about the same time, and you don't have part of your batch burning before the rest are done).