This proposed synth is not supposed to be a well... efficient or in good yeilds, just a proposal to see if it is possible.
Styrene + Br2/CCl4 --> 1,2-dibromophenylethane (A)
A + 2NaNH2/NH3 --> phenylacetylene (B)
B + NaH or NaNH2 --> sodium phenylacetylide (C)
C + MeI --> allylbenzene
definitely long winded for the product, but just a fun idea.