Yes, the reaction should work. "Dibromohydrin" does not exist, you must be talking about the bromohydrin (prep of bromohydrin: https://www.thevespiary.org/rhodium/Rhodium/chemistry/asarone.wacker.txt (https://www.thevespiary.org/rhodium/Rhodium/chemistry/asarone.wacker.txt)
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I believe the chlorohydrin does not spontaneously rearranges to the epoxide, you probably need concentrated base and heat (read more in the above ref).
Here is more info: http://www.chem.ucalgary.ca/courses/351/Carey/Ch16/ch16-6-ans.html (http://www.chem.ucalgary.ca/courses/351/Carey/Ch16/ch16-6-ans.html)
Sorry, I forgot to mention that I heated the epoxide to 300C before testing with bisfulite. I'll run the sample with NMR to see what actually happened. I got a viscous syrup, smelling unlike asarone. Btw, I did confirm that the mixture of NaOCl with no acid left the starting alkene intact. (ie Post 236380 (https://www.thevespiary.org/talk/index.php?topic=12224.msg23638000#msg23638000)
(Chromic: "Re: anethole -> epoxide", Novel Discourse) did not work)
If I was to try this reaction again (assuming that acidic NaOCl doesn't work), I would use sodium bromide to generate bromine in aqueous DCM then react with the alkene to try and get the bromohydrin. I would not try to dissolve chlorine into DCM. That sounds like a very bad idea.