For small distances (below 10 km), assuming Earth is flat and I have initial Lat0/Lon0 and I have X(km), Y(km) distance From Lat0/Lon0, how can I calculate new Lat/Lon for the added X,Y?
You can't assume that the Earth is flat and provide coordinates in angular units.
But you can assume that the Earth is a sphere and make simple spherical trigonometric calculations.
Define a radius for the sphere, something like
R = 6371 km. (Mean radius)
lambda_1 = lambda_0 + ( X / ( cos( phi_0 ) * R ) )
phi_1 = phi_0 + ( Y / R )
lambda is longitude and
phiis latitude, in radians;
1 are start and end points.