A shooting foul can only occur when trying to shoot at the basket which will increase your own team's score.
Therefore, if you were somehow shooting at your own basket and got fouled, it would be the same as a normal non-shooting foul. You would not get free throws unless you were in the "bonus".
If you actually made the basket, I think it would be waved off because it is a foul on the team who the score would go to. So just as a basket does not count when an offensive player commits a charge (or other offensive foul), a "wrong-way" basket would not count when the defending team has committed a foul.
In fact, this is the most likely way that your scenario would occur. Player goes up for a rebound, is fouled and makes the ball accidentally go into the basket. Foul would be called with "no basket".
Here is the official definition of a "Field Goal Attempt" from the NBA (http://www.nba.com/analysis/rules_4.html?nav=ArticleList):
A field goal attempt is a player's attempt to shoot the ball into his
basket for a field goal.
Attempt to shoot the ball into "his basket" means the basket which would give his team points. Trying to shoot the ball into the other team's basket does not qualify under this definition and therefore does not count as a "field goal attempt".
Free throws are granted for fouls during a field goal attempt, so since "shooting at the wrong basket" is NOT a field goal attempt, no free throw would be given.
In another section of the same rules (http://www.nba.com/analysis/rules_12.html?nav=ArticleList) it says:
A personal foul assessed against an offensive player which is neither an elbow, punching or flagrant foul shall be penalized in the following manner:
(1) No points can be scored by the offensive team
Which I take to mean that NO TEAM can score points on a play where they also commit a foul.