I play Searing Blaze targetting my opponent and their 1/1 token. In answer, they get hexproof (by flashing in a Leyline of Sanctity for example). Will the token be killed?

Yes.

From the Gatherer rulings for Searing Blaze: “If either target is illegal by the time Searing Blaze resolves, it still deals damage to the other target.”

Also, this follows the general rules for resolving a spell (or ability):

Originally posted by CR 608.2b:

The spell or ability is countered if all its targets, for every instance of the word “target,” are now illegal. If the spell or ability is not countered, it will resolve normally. Illegal targets, if any, won’t be affected by parts of a resolving spell’s effect for which they’re illegal.

d:^D