I am trying to figoure out the conditions and choice of solvents and catalysts in order to run this synthesis.
This is straightforward. 4-Toluenesulfonyl Chloride is readily attacked by nucleophiles and allylamine is a good nucleophile.
Dissolve 2.05 equivalents of allylamine (or 1.05 eq allylamine and 1 eq of an tertiary organic base such as triethylamine) in dichloromethane, cool in an ice/water bath (reaction is exothermic) then slowly add 1 eq of 4-toluenesulfonyl chloride dissolved in dichloromethane. Leave it half an hour then wash the reaction mixture with dil HCl soln, dried the organic phase, filter and concentrate to give your product.