Yes...but not very much.
Flicker Strike, like most "single-target"/namelock melee attacks, is a Strike skill, a new category of skill that was added to the game in the 3.7 patch alongside Legion league. Strike skills, unlike their pre-3.7 behavior, are not truly single-target anymore. Instead, they hit a small-ish cone, whose exact location and dimensions are based on the skill's attack animation.
The size of this cone depends, in part, on your weapon range. You can read about how this works in the 3.7 development manifesto, or see a direct demonstration of the effects of weapon range on Strike skills in this promo video from the pre-3.7 hype period.
However, that video somewhat oversells how good attack range is for Strike skills - you have to stack a truly huge amount of the stat in order to get results like you see there. In practice, the ability for Strike skills to hit multiple enemies only really comes into play when fighting closely-spaced packs of small enemies. If you're playing Flicker Strike, you probably already blow up that kind of pack faster than you even notice it's there - that's what Flicker Strike is good at. In situations where you have trouble (against strong, single-target enemies), weapon range doesn't do anything at all.
Weapon range does not affect where you teleport when using Flicker Strike (you will still teleport right next to the enemy you're about to attack), nor does it affect how close you have to be to an enemy in order to Flicker to them.
My overall advice would be not to bother investing in weapon range for a Flicker Strike build.