Connecting 14/3 off of 3 way switch to 14/2 line for new outlet
Not possible for 2 reasons.
You don't have the right wires there
The problem with (traditional) 3-way wiring is that you don't have the voltages you need in the places you need them.

You need black, and white.
Generally, in 3/4 way switch circuits, always-hot and neutral are only available at the location the power enters the circuit.  But if that was your setup, you wouldn't be asking for help, would you? :)
The cure for this half of the problem is smart switches.  They need either 1 or 0 traveler wires instead of 2, allowing you to reclaim black to be an always-hot.
Kitchen receps can't serve anything else, and can't be 15A
Unless the microwave is a built-in, you are not allowed to install a receptacle in a kitchen unless it meets some rules.

It must be 12 AWG and 20A breaker
It must be a dedicated circuit that serves nothing but receptacles in the kitchen, pantry, dining room, breakfast nook etc.  (or ignitor/oven light on a gas oven, or a wall clock).

Since the circuit already powers a light, it can't add a kitchen receptacle to it.   Since the circuit is 15A, you cannot add a kitchen receptacle to it.
&quot;But my existing wiring doesn't conform with that!&quot;  Sure, that is grandfathered if the wiring was legal at the time it was installed.  However your new addition is not grandfathered and must comply with current Code.
The quasi-cure here is for the microwave to be a &quot;built-in appliance&quot; where the recep is behind the installed appliance and not accessible for any other purpose.