In this context, the phrase is used to request confirmation of the statement.
"The trip to Vegas is definitely goin down this summer, Stamp That"
At this time, each member of the conversation makes the decision on whether or not to 'stamp' the statment, thereby giving their approval.
When reserved for serious statements, this phrase gives them extra credibility.
"The Detroit Pistons are going to win the finals, you can Stamp that.."
This is a declaration made by the user to illustrate his confidence in the statement.