This should work - you'll probably need to use GET to send the data through a URL to the PHP script. The Flash could build the URL containing variables based on which seat is selected:
eg http://example.com/select.php?row=2&seat=k
select.php will get the variables $row and $seat from the URL and you can process them however you want.
Apparently you can make Flash use POST rather than GET if you sent it in a form but not being a Flash expert I do not know how this works.