According to the Kalki Purana, Sri Kalki will obtain the horse and his sword by propitiating Lord Shiva.
After offering His respectful obeisances to Lord Siva, who is very easily pleased, and worshiping him with devotion, Lord Kalki began to speak, keeping His mind fully under control.
Then Sri Kalki recites a Lord Shiva Stotram (It is found in the Purana's 2nd chapter).
The English translation of the Stotram is as follows:
Lord Kalki said: О Lord Sankara, you are the oldest of all, the husband of Gauri, the lord of the universe, the only protector of the living entities, and the shelter of everyone. Your neck is decorated with the serpent, Vasuki, you have three eyes and five heads, you are always absorbed in transcendental ecstasy, and you award liberation to your devotees I offer my obeisances unto you.
You are the lord of mystic yoga and the destroyer of lusty desires. Your form is fearful to behold, your head is always wet with the water of the Ganges, the matted hair on your head looks most enchanting, your forehead is decorated with a mark of the half moon, and you are the personification of maha-kala. I offer my obeisances unto you.
You frequent crematoriums in the company of ghosts and hobgoblins, and you carry a trident and other weapons in your Hands at the time of annihilation, the entire creation is burnt to ashes by the blazing fire emanating from your anger. The conditioned souls are born in this world under the influence of false ego, and their bodies are made of the five gross material elements. You are the lord of the mode of ignorance, and thus you are one of the directors of the material universe. Although you are involved in universal affairs, you always remain aloof from material association as you remain absorbed in transcendental ecstasy, I offer my obeisances unto you.
I worship Lord Siva, the protector of the universe and the Super soul of all living entities. He is always victorious, being a qualitative incarnation of Lord Visnu, and He delivers saintly persons by protecting the principles of religion. He is the personification of transcendental sound, a reservoir of divine qualities, and the possessor of great intelligence.
By your order the wind blows, fire burns, the sun distributes heat and light, and the moon, planets and stars illuminate the sky. I offer my obeisances unto you.
By your order, the earth sustains all moving and nonmoving entities, Indra showers rain, the time factor divides the duties of everyone, and Mount Sumeru, which is the shelter of the universe, remains fixed at the center I offer my humble obeisances to the universal form of Lord Siva.[the Stotram ends here]
After hearing these prayers, Lord Siva, being omniscient, appeared before Lord Kalki with Parvati and spoke to Him while smiling grandly.
The Phalasruti of this Stotram, as given by Lord Shiva, is as follows:
Anyone on this earth who faithfully hears the glorious prayers that you have offered me will achieve all kinds of perfection, both in this life and in the next.
If a student recites these prayers, his education will become fruitful, if a pious person recites these prayers, he will attain pious merit, and if a sense enjoyer recites these prayers, he will enjoy all kinds of sense gratification. Anyone who recites or hears these prayers will have all his desires fulfilled.
And, thereafter Sri Kalki will receive the horse and the sword as described in the following verses:
I would also like to present You this sharp, strong sword and so please accept it. The Handle of this sword is bedecked with jewels, and it is extremely powerful. As such, this sword will help You to reduce the heavy burden of the earth.
After hearing all this, Lord Kalki offered His obeisances and then departed for the village of Sambhala, riding on the back of the horse given by Lord Siva.
I am looking for this Stotram in Sanskrit so that it can be recited.