Eric H. said:
5E PC sheet. He can use a bonus action to either get a second attack (Martial arts) or spend a ki point for flurry of blows. So either 2 attacks or three...
A monk by RAW gets his normal attack (one or two attacks depending on level) and then can make an unarmed strike or two (flurry of blows) by spending a ki.
Eric H. said:Since it is a bugbear his unarmed strikes are affected by "Brute" which uses 2d6 for its damage.
So Unarmed strike +6 to hit 2d6+3 for damage.
Technically a monk's unarmed strike is not a melee weapon. See the errata:
Melee Attacks (p. 195). The rule on unarmed strikes should read as follows: "Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes."
Even if you ignore the errata the brute NPC feature shouldn't translate to PCs. NPCs are created differently and allowing a race to do significantly more damage than another would be very unbalanced.
Anyways, now that my DM balance side has come out here is how you'd do it:
First setup weapons like so (this is the first and second slot):

Then under the Character's "Attributes & Abilities" tab add the following abilities:

Check them to "Sow as Token Action" and Wallah! I, personally would choose to do the normal "Attack" and then add on an "Unarmed" if you flurry. You could instead use "Attack" and "Attack-w-flurry".