The first time the Rebbe mentioned the campaign of Kashrus was on Tes-Vov Tammuz 5735, Parshas Pinchas. The Rebbe suggested that this is the solution to the situation that was happening then, since, as it is explained in Seforim, the food and drink that a person consumes has an effect on him. Later in the Sicha, the Rebbe set up a fund to purchase Kosher Keilim.
Sichos Kodesh (Seif Hei) | Likkutei Sichos (Page 60-62) | Audio
A few days later, the Rebbe spoke about the initiative again connecting it to that week's Parsha, Matos-Masei. The Rebbe then said that just like this was the final Hachanah for the Dor Hamidbar, so too this is our Hachanah to go to Eretz Yisroel.
Likkutei Sichos (page 295-297) | Sichos Kodesh
A while later, on Yud Beis Tammuz 5737, the Rebbe spoke about all the Mivtzoyim and spoke about the idea of Mivtza Kashrus, discussing a new cook book that was published for Hafatza.
Sichos Kodesh (Seif Nun) | Audio
The following year, on Parshas Vayakhel 5738, the Rebbe described Mivtza Kashrus, that the blood and flesh of a person should be made of Kosher food.
Sichos Kodesh (Seif Yud-Daled) | Audio
On Vov Tishrei 5745, in connection with the twentieth Yahrtzeit of Rebbetzin Chana, the Rebbe requested that twenty new Mikvaos be constructed, and that twenty new funds to assist people in Kashering their kitchens, as well as twenty new funds to encourage Neshek be established.
Sichos Kodesh | Toras Menachem | Audio | English
Letters of the Rebbe: Learn, discover, and bring meaning to the mitzvah of Kashrus