If i have sexual intercourse with the same person after we've both been treated with chlamydia can we get re-infected?

Less likely: If both of you have treatment in the same time and recheck it negative. Then recurrent is unlikely.

Chlamydia Treatment: Most treatments for chlamydia are effective. As long as you both waited for the treatment to be effective it is likely that you won't get re-infected. However, if you have any further symptoms re-testing is common and a good way to be reassured.