You can't add a cooldown easily, but you can modify the bonus damage if you go into xcomlw_perkpack.ini and look for

[LW_PerkPack.X2Effect_FlecheBonusDamage]
BonusDmgPerTile=0.334f ; extra to handle round-off errors

replace 0.334 to increase/decrease the bonus damage per distance moved.

Imo the issue isn't the lack of a cooldown but rather that it gives the same bonus to a squaddie with a basic sword as a brigadier with a fully upgraded weapon.

Cheers, I'll give it a look. That is a good point, but the other issue with Fleche is that Reaper doesn't seem to affect its damage and accuracy at all. I had a mission the other day where my Shinobi managed to plow through 16 out of 20 of the enemies on the map in a single move, including advanced ADVENT troops and MECs, because even by the end they were able to do 20 damage with a guaranteed hit.

But should still not be used against Mutons, Sectopods, Gatekeepers, Avatars, and Hive Queens.

Yes, it is OP until you activate a pod carelessly and the Shinobi dies because of it. :-) High risk high payoff perk.

What difficulty were you playing on? Hope it is Legendary, I can't wait until I get my hands on a high lvl Shinobi. :-)