I tailor it to who I'm with: mostly little kids at church. My usual thing is take what they're doing, and bump it up a notch.
I play with them in public areas, in front of other people/ their parents - QM, sloth hang from railings, play 1 foot hopping chase, climb on trees, jump around. I'll throw in a couple vaults maybe. Depends what's around, how safe it is, age and ability of the kids, etc.
Since you're in a gymnastics gym... and the people are asking you for parkour basics...
1. Jump tests are good... When they're doing the high jumps, emphasize good landing technique.
2. Monkey and kong can be hard for people with less upper body strength. First I'd have them try a 2 hand vault, then lazy, then speed.
3. Then I'd try the monkey up and kong. If they're weak, I'd have them do QM. Especially good if you have a low balance beam they can cat crawl on, and something they can QM under. You may want to show the roll before teaching the kong?
4. I'd skip the dash.
5. Precisions are good. I like to throw a couple pennies on the ground and have them try to precision onto the pennies. After a few shots, have them precision next to, but not on the pennies. When they know it's spotting safe/ unsafe places to land, they don't mind so much. Move them around, increasing the difficulty. Bonus if you can show them how to crane if they under-jump.
6. Is there any place to do a 5 to 6 foot wall-up? Teach them how to pop it first, then how to cat and pull up [if they have the upper body for it]. Also show them proper ways to get down. [Hang and drop, squat and 1 hand to guide/ slow the landing, "1 hand dash", etc].
This would cover 80% of the basics of parkour: landings, rolls, jumps, QM, the angled vaults, the straight on vaults, precisions, up and down walls and cats. If they have the ability and desire to get fancier than that, let them try, but if there's too much slop, make them break down the move so they're forced to do a few good landings, etc.
Because this is a gymnastics gym, you'll probably have plenty gymnasts. I would actually encourage chaining together moves [flow] before I would teach flash... [but for me, that's maybe because I can't DO the flash

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