"The only way to get rid of a temptation is to yield to it. Resist it, and your soul grows sick with longing for the things it has forbidden to itself, with desire for what its monstrous laws have made monstrous and unlawful."
The studio was filled with the rich odour of roses, and when the light summer wind stirred amidst the trees of the garden, there came through the open door the heavy scent of the lilac, or the more delicate perfume of the pink-flowering thorn.
Dr. Chasuble means that he, like Ernest who supposedly died of a severe chill, is susceptible to a current of air ("draught" is the British spelling of "draft"😉. Wilde is punning on "draught" to suggest Dr. Chasuble is also susceptible to "a serving of drink, usually alcoholic, drawn from a keg." This is evident by the previous line that "none of us are perfect." Another pun, although rather meaningless, could be on the British recognition of "draughts" as the game of checkers.
“You can't possibly ask me to go without having some dinner. It's absurd. I never go without my dinner. No one ever does, except vegetarians and people like that.”
― Oscar Wilde, The Importance of Being Earnest