The stories of Kalki are largely symbolic as is evident from the images of the white horse (symbol of the Divine Force) and the sword (of knowledge). Parashuram ji is a fierce form of Rama that destroys darkness with the might of Kali. Obviously he will not train Kalki Avatar into the art of weilding the Divine Axe (that was useful at that time) but instead arm the Kalki Avatar possibly with the power to write (more appropriate to our times). We should see these stories in the total context and with the symbol they contain.
Affectionately,
Alok Da