The Lord has never given a revelation on fast offerings. The doctrines pertaining to the concept of caring for the poor in relation to fasting are individual instructions, not connected to an institution. Both the commandment and the promised blessings are individual.
Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke? Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh? Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the Lord shall be thy rearward. Then shalt thou call, and enumerated on the sheet, which would not have caused money to be spent by the church. the Lord shall answer; thou shalt cry, and he shall say, Here I am. If thou take away from the midst of thee the yoke, the putting forth of the finger, and speaking vanity; And if thou draw out thy soul to the hungry, and satisfy the afflicted soul; then shall thy light rise in obscurity, and thy darkness be as the noonday: And the Lord shall guide thee continually, and satisfy thy soul in drought, and make fat thy bones: and thou shalt be like a watered garden, and like a spring of water, whose waters fail not. (Isaiah 58:6-11.)
In principle, the church’s fast offering program could be used to facilitate mobilization of resources from affluent members to areas of the world that are more destitute. In practice, since the church’s fast offerings are encouraged to be consumed locally, and since it takes approval from the stake, area, and presiding bishop levels before funds can be obtained from headquarters, the fast offering program does not have many advantages compared to the scriptural practice of individuals directly donating their money to needy parties. In fact, given the abundance of all-volunteer organizations who care for the poor internationally, it could be argued that direct contributions through international charities have greater impact on the plight of the poor than traditional church fast offerings, which are almost guaranteed to be consumed locally in comparatively affluent areas.