does the phrase”direction of zero vector” have physical significance? discuss in terms of velocity and force

No. the zero vector has no direction, therefore it has no significance.

Yes the phrase keeps enough importance in real. Now think that you have applied a force on a box which does not move in any direction. Means its vector of velocity as well as acceleration becomes zero. This became very easy to discuss. But the same thing cannot be represented easily in mathematical terms. So here zero vector will come to your aid.F = maWhere a is an acceleration with zero magnitude but will be in the direction of your force once achieve some magnitude. Now in this sense, acceleration has direction but no magnitude or zero magnitude.Therefore F = m(0) = 0N