If I use flurry of blades deal 1 damage to 7 might unit. Can my unit with 6 might can kill it?

Yes — 6 damage is enough, because the 1 damage already marked counts toward lethal. Lethal is a total of marked damage equaling or exceeding Might, not a per-assignment amount, so you only need to assign the remaining 6 to reach 7 (Rules 142.4.b, 465.2.c.4; FAQ #4107/#8364).

So in that Combat Damage Step your 6-Might unit assigns 6, the 7-Might unit now has 7 marked, and it dies in the cleanup. Note you may assign only the 6 — you can't be forced to over-assign.

Two caveats: the Flurry damage must still be there (a Combat Cleanup heals all units in play, and damage also heals at end of turn — if a combat resolved in between, the 1 is gone and you'd need the full 7), and the unit must still be at 7 Might at that moment. Also, damage is dealt simultaneously, so if it's a real combat, that 7-Might unit is still dealing 7 back at your 6-Might unit — killing it too.