If we have two interacting gases of different temperatures, then it
may be possible that a packet of particles(*) which move at high speed...
In a "packet of particles" the individual particles will not all move at a "high speed". If the packet of particles is large enough, then the speeds of the individual particles will vary about the average speed of the packet of particles according to the Stephan-Boltzmann distribution of the speeds about the average.
...go from the hot gas into the cold one (by chance) and raise the
temperature of the cold gas by transferring heat.
Not sure what you mean by "go from the hot gas into the cold one (by chance)". But individual particles of the high temperature packet of gas will collide with individual particles of the low temperature gas. On average in the collisions there will be a net transfer of kinetic energy from the high temperature particles to the low temperature particles simply because the average kinetic energy of the particles of the high temperature gas is greater than the average kinetic energy of the particles of the low temperature gas.
However, it is said by the Clausius statement of the second law the
heat only flows from a hot body to cold, so the situation outlined
must be a violation of the second law.
There is no violation of the second law. Although there may be energy transfer from collisions of higher speed particles of the lower temperature body to lower speed particles of the higher temperature body, the net transfer involving collisions of all the particles will be from the higher temperature body to the lower temperature body.
Before people tell me that temperature is an emergent property,
consider a packet of particles large enough for the temperature to be
definable, if this does mean that the second law of thermodynamics
holds only when considering the macroscopic picture? Or is the second
law saying is that it is not possible for such a 'packet' transfer to
If the packet of particles is large enough for the temperature to be definable, that is, for the Stephan-Boltzmann distribution to apply, then the net transfer of energy is from the packet having the higher average kinetic energy (i.e.,higher temperature) to the packet having the lower average kinetic energy. That, however, does not preclude the possibility of energy transfer from some high energy particles of the low temperature packet to some low energy particles of the high temperature packet. That does not violate the second law.
Hope this helps.