First, check and see if the site has an app available, if so, use that.
Second, check to see if the station is covered by the iHeartRadio app. They cover about 1000 live station feeds.
If not, you can TRY iSwifter, Skyfire, Photon, or Rover -- those browsers attempt to recognize Flash content and then work out a way to play it (basically, they are browsers built on Adobe Flash then compiled into a native iOS app - nearly all Flash content SHOULD be accessible).
Adobe dropped support for Flash on mobile a year ago. iOS never had Flash support, and it was available for a time on Android and is now gone again.
Since Flash isn't technically necessary for live radio apps, presumably sites that use them it that way will switch over to HTML5 or services like iHeartRadio.