Are inflict and afflict in conflict? Quite a few commentators think so, and they warn us not to confuse the two. As is often true in these cases, the confusion is imaginary. What is perceived as confusion is in fact persistence of the oldest sense of inflict, which means the same as afflict.
Inflict typically occurs in constructions in which something is inflicted on, or upon, somebody:
... once in a great while I inflict it upon people — Thomas H. Middleton, Saturday Rev., August 1981
... I am resolved not to inflict boredom on even the most deserving —Oliver St. John Gogarty, It Isn't This Time of Year At All!, 1954
... a model knight on whom God suddenly inflicts leprosy—Times Literary Supp., 1 Dec. 1966
Afflict typically occurs in constructions in which someone is afflicted with or by something:
I found myself afflicted with a sense of the staleness and glibness of my verse —Donald Hall, Goatfoot Milktongue Twinbird, 1978
Evelina is afflicted by a sense of responsibility for actions which she opposed —John Butt, English Literature in the Mid-Eighteenth Century, edited & completed by Geoffrey Carnall, 1979
... how a composer's work is both aided and afflicted by the power of record companies —Lang-don Winner, N. Y. Times Book Rev., 17 April 1983
These are not the only constructions in use, but they are typical. And they match the guidelines set up by the commentators. The thing to note is that the typical direct object of inflict is some unpleasant circumstance and the typical direct object of afflict is a person. The older sense of inflict works just like afflict:
The miners are still out, and industry, as a result, is inflicted with a kind of creeping paralysis —Harold J. Laski, letter, 30 May 1926
... a sick man inflicted with an incurable ailment — Manchester Guardian Weekly, 20 Nov. 1936
... inflicting us with a meddlesome cub —Warwick Deeping, Sincerity, 1934
The dates of the examples, our most recent, are worth noticing. Maybe this older use is passing away, but we cannot be sure. At any rate it has never been very common, and we do not recommend that you try to resurrect it.