The general problem with wanting to get into arcane duelist ASAP is that all the base classes that have actual synergy have 3/4 BAB (like most of the good classes in the game). That said, if you want to do it, there are only two base classes with full BAB and arcane casting, hexblade and duskblade. Hexblade sucks in general and particularly sucks for arcane duelist since almost none of its features do anything for melee. Duskblade doesn't suck in general, but all of its non-spellcasting features help its casting and arcane duelist doesn't advance casting, so you want 1 level of duskblade to meet arcane duelist's prereqs and then to move on to other classes that will help you do damage in melee or improve your utility. If there were some PrC that you could enter at 6th level with its own arcane casting and full BAB, that would also work, but I don't know of any such PrC. You can easily fill out the rest of the classes by asking, "What base classes don't totally suck and have full BAB?" The list is barbarian, crusader, ranger, and warblade, with maybe fighter as a 2-level dip and swashbuckler as a 3-level dip (barring a certain combination feat with rogue, which is out here because it has 3/4 BAB). The goal, then, is to use those class levels to optimize either dexterous attack with Power Attack or false keenneess, with an eye to doing damage with flurry of swords.
Route #1: Dexterous attack, Power Attack, Leap Attack, Shock Trooper, Combat Brute, and pounce. You're already planning to use Power Attack, so why not increase Power Attack returns? You don't strictly need Shock Trooper since with dexterous attack you're going to be Power Attacking to the limit of your BAB anyways, but with Shock Trooper you can get high attack bonus and damage; if you do take it, you might as well ignore Cha because your AC's going to be minimal anyways. To support the feats you'll need fighter 2. Barb 1 with the lion totem ACF (CC) is the best and probably only way to get pounce. Ranger doesn't do anything for this build, so the other 2 levels should probably be warblade or crusader. If you're into futzing with weird races, you can use raptoran (RW) or a dragon-blooded race (DM) with the feats Dragon Wings and improved Dragon Wings (RDr 100) to do the same thing with dive attacks, though swinging the feat costs will be brutal. For utility, you'll have to lean on skills and an appropriate stance, probably hunter's sense if you can meet the prerequisite.
1: barbarian; Power Attack
2: fighter; Dodge
3: fighter; Mobility, Improved Bull Rush or Improved Sunder
4: duskblade
5: warblade or crusader
6: warblade or crusader; Leap Attack
7: arcane duelist
8: arcane duelist
9: arcane duelist; Combat Brute or Shock Trooper
If you're human, you can build up to the top feats sooner.
Route #2: dexterous attack/Power Attack with TB stuff. TB classes don't have particularly outstanding damage except for swordsage, but you can try to pile up bonuses. Standard-action strikes and the dexterous attack/Power Attack combination don't work well with only two exceptions, diamond and ruby nightmare blade, but you can't get those without taking Martial Study at high levels. Crusader 4 for furious counterstrike and steely resolve 10 will get you some damage, as will punishing stance. The route with the highest potential damage is Stormguard Warrior but as always Stormguard Warrior has a lot of problems. For channel the storm, you need Combat Reflexes and ways to make enemies provoke AoOs, which don't fit naturally into this build. You have Dodge so Karmic Strike isn't as painful as for most characters, but it and Robilar's Gambit are still very limiting as strategies since they only help against enemies that hit you in melee and straight-up trading hits with monsters is usually not a good idea. For combat rhythm, you need the ability to spam attacks, which for this character probably means TWF and in turn conflicts with the dexterous Attack/Power Attack combination. There are ways around this (Oversized TWF), but they still end up losing reach and costing lots of feats. Note that all of these approaches except combat rhythm rely on your getting hit, penalize your AC, or both, so are anti-synergistic with getting Cha to AC. Crusader and warblade also don't do much to help your utility. Your build is probably going to want to be crusader or warblade 1/duskblade 1/the other of crusader or warblade 4.
Route #3: false keenness, Improved Critical, some form of keen, TWF, blood in the water, and proc-on-critical-abilities. Your goal is to stack up blood in the water as fast as possible because it's your primary damage source. You almost certainly want to dual-wield kukris unless you plan to include Power Attack and Oversized TWF with scimitars or rapiers, though that gets quite feat-intensive. Warblade 3's battle ardor is an easy bonus to critical confirmation if you have good enough Int, but you may still want Power Critical or something else. The big choice is whether you go warblade 1/duskblade 1/warblade 4 or ranger 2/warblade 3/duskblade 1. Ranger will give you some extra utility from better skills and free Track plus TWF and a favored enemy, while warblade 5 will give you another stance, more maneuvers, and a bonus feat that will be less directly useful. Staggering Critical (DU) is a great feat to take later. You'll need to find ways to get criticals on monsters normally immune to them, like deathstrike bracers or greater demolition and truedeath crystals from the MIC.
