Here the words "know" and "am persuaded" mean basically the same thing; Paul uses them to emphasize his certainty. AT: "I am certain because of my relationship with the Lord Jesus" (See: [[rc://en/ta/man/translate/figs-doublet]])
Paul implies here that a person should stay away from anything that he thinks is unclean. You can make this explicit in your translation. AT: "But if a person thinks something is unclean, then for that person it is unclean and he should stay away from it" (See: [[rc://en/ta/man/translate/figs-explicit]])