Under the official rules: No, you may not uise a tumble check to move in a prone position.
If begin the round in a prone position, you have a few choices under the current rules:
1.) Stand up as a mvoe equivalent action that provokes an AoO,
2.) Crawl 5' as a move equivalent action that provokes an AoO, or
3.) Use the epic rules to make a DC35 tumble check to stand as a free action. Note: There is a trend in 3.5 to not provoke AoOs on free actions, though this is only a trend and note a firm rule (the PHB pg 144 says, "Free actions rarely incur attacks of opportunity.") Standing as a free action is never listed as not provoking an AoO, but it seems to follow from the text that it should not provoke an AoO. It would need to be a house rule at this point, but it seems like a house rule with good support.