We do this quite a bit here. And as other here have mentioned, make your original cts as straight as possible. We then sand it with 80 grit, then 120. Then flame polish it with either pure oxygen or with a small butane torch. Just let the flames 'lick' the acrylic to prevent bubbling. and then whatever you do...DO NOT CLEAN IT WITH ALCOHOL AFTERWARD!!!! It WILL crack and you're piece will be no good. Learned this one the hard way...A couple times (ughhh...bad memories).
I do love the look of flame polished acrylic though. Also, for higher production (if you plan on doing this a lot) - you can build a 'slider table' (in house name for it) - Basically just a 4' x 6' piece of plywood on a slight angle (maybe 10-15 degrees) with a non slip surface (tool box drawer stuff). This assembly is attached to another 4' x 6' piece of plywood at the same angle and a series of standard kitchen drawers sliders to allow the 'slider table' to move 3' right and left, for a total of 6' of slide. Then we have the oxygen torch on a fixed stand aimed at the bottom of the top piece of plywood's bottom (right where the acrylic panel is located) - Then we just load the acrylic on the board - turn on the heat - and slide the acrylic quickly across the flame. We do this about 3 or 4 times until the edges are done properly. (You can also place a piece of angle iron or aluminum at the bottom of the slide portion of the table to prevent burning of the wood when you're doing high production - if not just let the edge of the table cool slightly before moving on to the next edge)
Once the 'slider table', or 'flame table', is complete - it only takes about 1-2 minutes to do all four sides of jut about any size panel you wish....
Hope this helps and wasn't too confusing.
Cheers,
Chad