Try changing your code in the following way for MySQL:
BEGIN
IF EXISTS (SELECT * FROM chars WHERE accid = NEW.accid) THEN
INSERT INTO `char_vars` SET `charid` = NEW.charid, `varname` = `NotFirstChar`, `value` = 1;
END IF;
INSERT INTO `char_equip` SET `charid` = NEW.charid;
INSERT INTO `char_exp` SET `charid` = NEW.charid;
INSERT INTO `char_jobs` SET `charid` = NEW.charid;
INSERT INTO `char_pet` SET `charid` = NEW.charid;
INSERT INTO `char_points` SET `charid` = NEW.charid;
INSERT INTO `char_profile` SET `charid` = NEW.charid;
INSERT INTO `char_storage` SET `charid` = NEW.charid;
INSERT INTO `char_inventory` SET `charid` = NEW.charid;
END
Also if your NotFirstChars
meant to be a constant string (not a field name) you should change the quotes: 'NotFirstChars'