I just got back from visiting there a few days ago and spent a large portion of my life living there. You can still fish but it is catch and release only. Oil was showing up on the Gulf Shores beaches but none so far on Dauphin Island. Lots of Ladyfish and Sand Trout (like a Speckled Trout) to be caught. Although I didn't catch any, Bluefish should be showing up. Also saw more sharks along the beaches than I have ever seen! Be careful in murky water and dim light.
Some of the better spots are like the Cut going into Little Lagoon are serving as staging areas for clean up crews (thousands of people) so there is little or no access to them. I would try the Fort Morgan Pennisula, either the Gulf side if the oil/surf isn't to bad or the point. May even pick up a few Reds along there. If the conditions aren't good there there is losts of wading on the Mobile Bay side of the Pennisula around the Edith Hammock area.
No fly shops on the Gulf Shores side of the bay that I know of but there is a nice Bass Pro Shop in Daphne. Go see Jonathen in the fly fishing section and he'll give you some good advice. Everything I caught was on a fly called a Kingfisher Spoon, hot pink and gold. Looks like a bugger to cast but its not. I used a 6 wt with a clear camo line, plenty of rod for anything inshore (except the sharks). Strip it in, fast as you can, and hold on!
Oh yeah, Jimmy Buffet is giving a free concer on the beach July 11, it will be a madhouse!