As with any credit card, there's a risk you'll be denied. In such a situation, if you're confident you have good credit, you might consider applying for a balance transfer card from a different issuer than the one that denied you. Or, you could apply for a personal loan to pay off your credit card debt instead.
If you have poor or fair credit, you probably can't get a balance transfer card from any issuer. And if you get approved for a personal loan, it's likely to have a high APR. In such situations, you might wish to work with an accredited nonprofit debt counselor to put together a plan for paying down your debt. After following through on such a plan and paying off your debt, you might consider applying for a secured card to help improve your credit score.
It's a long journey, but there is no quick fix in such cases.