Why is it so expensive flying from Paris to Los Angeles?

I ticked the box both from Chrome and KLM iOS App - didn't show any flexible fares. Are you located in the States?

If you ticked the box, then you're getting Flex fares. click on the "Ticket Conditions" link beside each flight on the flight results page. You should get the same conditions in a pop-up box that I posted inline above.

I just tried again. I also noticed your screenshot does not have the text "Refundable if you cancel before the 1st flight in your trip"

different text but same conditions...
"refundable in case of cancellation before flight departure" means the same thing (they are talking about the 1st flight). Note that this means you can't cancel the ticket once you've started travel (this is normal, though); so once you got to Europe, you can't cancel the CDG-LAX flight for full refund (but why would you want to do that?). In that scenario, they would *probably* re-price the journey the corresponding one-way LAX-AMS fare applicable on the date of purchase and refund whatever was left over from the amount you paid for the open jaw but don't hold me to that without seeing the full Fare Conditions.

Compare with the conditions if you don't tick the "Flex only" box:

Then that makes more sense. The difference of the text threw me off. My thinking is if the airline cancels, it is then refundable. Thank you.

If the airline cancels a flight, consumer law would dictate that you can always get a refund (if that's what you want) even if you opted for the cheapest, most restrictive ticket not allowing the passenger to make any changes or exoect any refunds if they didn't fly or requested cancellation.

The Ticket Conditions as shown above regarding whether a ticket is refundable refer only to voluntary requests spontaneously made by the traveller for their own personal reasons.

Something is definitely wrong with the iOS App. Went through the same steps. I think I just need to use browser on laptop.

I was getting frustrated recently by not being able to find a one way flight that fit my needs for under 330 odd EUR with three weeks lead time.

Until I remembered not to be an idiot and bought the same connection out, but with a return in three months, for under 250.

You dont really need to tick that box.

Just search for your fare normally and pick Flex option when it says "select your fare" which should be available on all tix.

When using the Multi-City option to book an open-jaw at the destination, you don't get to choose between fare types; so when you want a Flex fare, you have to tick the box.

That's the reason why the Flex box is shown when you select Multi-City.

Ah I get it now, my bad.

LAX-AMS roundtrip will be less costly than LAX-AMS CDG-LAX
Air France has no Z class for your dates for the Paris-LAX leg so there is a premium there.

Is there a site that describes the various classes like Z?

I once forced Trip.com to put me back on CZ J, using money from their pocket, from a cancelled return flight on WY J(SIN-CAN) that was cancelled 2 weeks in advance, Trip.com initially offered to just cancel the ticket together at a full refund rate. Obviously, as every man will, I rejected their offer(dude, I paid 600SGD for SIN-CAN RT in J, how on earth can I book that anywhere else?) and said I will that the legs when possible, and opted for them to put me back on SQ for the CAN-SIN leg in J. They rejected the offer back, saying that their superior won't allow them to do so, however, we eventually settled on CZ J for the return leg at no extra charges on us, but I guess they lost a huge amount of money on this as the CZ leg Trip.com booked us back on "J" fare code, full fare J rate, and earned a whopping 250% CZ points. Still, anyways, despite the expensive CZ leg for them, the CZ flight was way inferior to the WY offering as WY offer Dine-On-Demand, along with fully lie-flat on the A330. At the same time, CZ flies a bunch of assorted narrowbodies 4 times daily to SIN with recliners in J.

But yeah, the process was very tedious, I threaten them to the extent of not doing business with them again, as I have spent more than 100K with them anyways.

Z is a business class fare class, so it's not relevant to your ticket or to this discussion - as I understand it, you are booking Economy.
Behind the scenes, the airlines have various different price points at various different "hierarchies"; they use letters of the alphabet to help segregate each cabin into numerous different price points. In business class, AF typically uses J, C, D, I and Z. Premium Eco fares use W, S and A. Economy fares use Y, B, M, U, K, H, L, Q, T, N, R, V. In general, in each of the listed cabins, prices decline (and conditions become more onerous; advance purchase, less flexibility etc) as you move rightwards through the given letters.
It's not something the average traveller needs to worry about or concern themselves with.