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You can actually use Emirates miles on a number of partner airlines, including Alaska, JetBlue and Virgin America, but the number is really limited and you won't find a major US airline on the list. We would advise you to use Emirates miles on Emirates flights as the transfers are rarely 1:1 and there's a possibility that you'll lose some portion of rewards on transfers.
Airline rules are really strict sometimes, they try to tie you to themselves or partner airlines, cause it's not profitable for them to channel your money elsewhere.
There's a way around it, though. A travel credit card can let you earn miles that you can redeem on any airline of your choice. Such credit cards also make accruing miles much easier as they let you earn not only on flights, but on all other purchases. One good example is the Discover it® Miles. There are virtually no limits on this card. You can earn miles on any purchases and redeem on any purchases, and more importantly, there's no limit to how many you can earn. Miles never expire, so you can earn a ton of miles and then redeem for a super long super expensive roundtrip flight.
The rewards rate is also pretty good, you get 1.5 miles for all purchases and the first-year miles are matched at the end of the first year (provided you are a new cardmember). Discover has no annual fee and no foreign transaction fee, it's one of the cheapest cards to maintain. And if you want to take that super expensive flight, you can do it right now, as the Discover it® Miles has 15 months of 0% intro APR on purchases, so you can go now and pay over time. Note that when the introductory interest rate is over, then 17.24% - 28.24% Variable APR on purchases will apply.