clustering (lat,lng) pairs, with clusters having the same number of elements
This sounds like it may be a NP-hard problem. But perhaps a relatively simple heuristic will give good enough results, something like:

Use one of the heuristic approximations to the travelling salesman problem to find a (relatively) short loop that passes through all of your N locations.
Then arbitrary pick some location on that loop as a "starting" point location number 0, and number each location along that path from 0 to (N-1).
Each employee i (from 0 to k-1) gets the approximately N/k consecutive locations along that loop, from location i*N/k to location (i+1)*N/k - 1.