Proof of Burn lets someone buy into an Alt Coin.
How is it policed so that someone doesn't "double-spend" by using the same Proof of Burn to simultaneously buy into Alt Coin 1 and Alt Coin 2?
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One approach to proof of burn is that you burn coins by sending them to a particular address specified by the altcoin. For instance, with Counterparty, you could collect XCP by sending bitcoins to the "burn address"
1CounterpartyXXXXXXXXXXXXXXXUWLpVr, thus making the bitcoins unspendable. Presumably no other altcoin is going to choose that particular address as their burn address, so there is no way you could earn any other currency by burning coins in that manner.
Of course, someone could have started another currency (call it PDQ) that awards credit for coins burned to the Counterparty address, and then people sending coins to the Counterparty address would earn both XCP and PDQ. I don't know of any reason why anybody would want to do that, or why anyone should expect the hypothetical PDQ currency to pick up any value.
Your reference to "double spend" suggests something different: that you might try to send bitcoins to the burn address for some altcoin, collect your altcoin reward, and then use a double-spend attack to reverse your burn transaction and keep the bitcoins after all (perhaps later burning them for a second altcoin). As Andrew Chow says, the first altcoin should prevent this by waiting to award the altcoins until the bitcoin transaction has sufficiently many confirmations.