The easiest way if you need to book right away is apply for the Barclay Arrival+, get it, and just pay for the flight on that, and they reimburse you travel costs ($500 IIRC?), once you've hit the minimum spend amount, even travel expenses up to 90 days in the past. So you can get the card, book the ticket, then after your trip hit the minimum spend and get reimbursed.
The Capital One Venture card is similar in how it works, but only gives you $460, IIRC.
There are other ways to get the miles, but if you're on a tight timeframe, that's the way to go.. then start earning the miles ahead of when you need them (cause typically you need to apply for the card, receive it, hit the minimum spend, wait for the statement to close, then the bonus to post, THEN you can use it.. takes at least 1-2 months).