The fundamental reason this happens is that Index Funds aren't "real" stocks. You cannot really sell SPY. There is a bucket of shares owned by SPY. Those contain shares of the index' companies. There's an "owned by clients" bucket and there's a "share liquidity reserve" bucket (with shares of companies in the fund). There's also a (small) liquidity "bucket of cash".
And of course, that company can, subject only to it's own chosen limitations, "print" SPY shares and sell them. So there's never any shortage of those.
When people transact in SPY, the trades are satisfied from those buckets. The cash bucket for investors selling SPY, the reserve shares bucket for investors buying. Those buckets are then refilled by the firm behind SPY buying and selling shares so that their share reserve and cash reserve remain at useful levels.
But let's now say there's heavy selling, for whatever reason. Sells really exceed buys and ... the cash bucket runs dry. Well, now sales stop, potentially indefinitely. The company will try to refill that bucket quickly, but there's absolutely no guarantee they will succeed, and there's no timeframe. Because the price for redemptions is only determined when they refill the bucket, you have no control over when this price is determined. It could be days after your order went through. Most index funds also technically have the right to just suspend redemptions entirely, indefinitely. Because of the amount of money in index funds, this will exhaust liquidity on actual shares relatively quickly and the whole market will freeze (because: no buyers)
Burry's claim is that if this ever happens, and investors find themselves stuck in index funds with no way out, there is nothing that will resolve that situation. Buyers won't want in, because once in, no way out. Sellers will panic and REALLY want out. This situation will self-reinforce until the market is driven into the ground.
0. some random situation causes that sellers exceed buyers for an index fund enough to initially exhaust the liquidity buffer of that fund
1. liquidity buffer in an index fund is empty
2. because of this transactions in the index fund stop
3. this causes panic, meaning less buyers, more sellers
4. goto 1, with situation getting worse every iteration
It won't be a "flash" crash, you'll just be locked in your index funds until the crash is complete.
It's hard to argue that this situation is impossible, that it cannot develop. It also seems to me that his conclusion that if this ever happens, it'll self-reinforce is correct. That said, we are pretty far from this happening.