John Gill Commentary Deuteronomy 12:15

"Notwithstanding, thou mayest kill and eat flesh within all thy gates, after all the desire of thy soul, according to the blessing of Jehovah thy God which he hath given thee: the unclean and the clean may eat thereof, as of the gazelle, and as of the hart." — Deuteronomy 12:15 (ASV)

Notwithstanding, you may kill and eat flesh in all your
gates
They might kill such cattle that were allowed for food, and eat the flesh of them in their own cities and houses in which they dwelt; they were not obliged to bring these to the place God should choose, and kill them there, as they had been accustomed to bring them to the tabernacle while in the wilderness:

whatsoever your soul lusteth after ;
whatever they had a mind to, or their appetite craved, and were desirous of, provided it was not any thing forbidden, but was allowed to be eaten:

according to the blessing of the Lord your God which he has given you ;
which it was in the power of their hands to procure for themselves; they might live according to their abilities, and keep a table answerable to what God had blessed them with; from which they were so far from being restrained, that it was rather commendable in them so to do, provided they did not indulge to luxury and intemperance:

the clean and the unclean may eat thereof ;
that is, such in their families who laboured under any ceremonial uncleanness by the touch of a dead body, or by reason of issues and menstrues; these, as well as those who were free from anything of this kind, might eat of common food in their houses, though they might not eat of the holy things; see (Leviticus 7:20Leviticus 7:21)

as of the roebuck, and as of the hart ;
that is, as those were clean creatures, and allowed for food, (Deuteronomy 14:5) so they might eat of oxen or sheep, or lambs or rams, and goats, though they were creatures used in sacrifice.