No. The Attack action is a specific action that you take in combat, which can include multiple attacks. From page 71 of the Player's Basic Rules:

Attack

The most common action to take in combat is the Attack action, whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists. With this action, you make one melee or ranged attack. See the “Making an Attack” section for the rules that govern attacks. Certain features, such as the Extra Attack feature of the fighter, allow you to make more than one attack with this action.

The important distinction to understand here is the difference between "the Attack action" and "an attack". Flurry of Blows can be used after you take the Attack action, not after an attack.

So you take the Attack action, using Extra Attack to attack twice, then you can spend a ki point and use your bonus action to attack twice with Flurry of Blows.

It should be noted that even if Flurry of Blows could be used after an attack rather than after the Attack action, it still requires a bonus action to use, and you can only use one bonus action per turn.

Attack bonus

• +2 BAB (from 3 levels of monk)
• +3 Dex
• -2 Two-weapon fighting with a light weapon in your off-hand (unarmed strike)

+3/+3

Attack bonus with a Flurry of Blows

• +0 BAB (from 3 levels of monk, Flurry of Blows column. You don't add it, you use it instead of your usual BAB whenever you use the Flurry.)
• +3 Dex
• -2 Two-weapon fighting with a light weapon in your off-hand (unarmed strike)

+1/+1/+1

Damage bonus

Depends on your Str bonus. Let's assume +2

• For two handed weapons it's 1.5 times your bonus, rounded down.
• For unarmed attacks it's your bonus, because monks don't halve it.

So:

Attack 1 (spiked chain, main hand, finessable, reach)

• 1d20+1 to hit
• 2d4+3 damage

Attack 2 (unarmed, finessable)

• 1d20+1 to hit
• 1d6+2 damage

Attack 2 (unarmed, finessable)

• 1d20+1 to hit
• 1d6+2 damage

Horrible, I know. But that's what you get when trying to use early on features and feats that decrease your chances to hit in order to get you more attacks.

A note on weapon proficiency

In 3.5e if you're proficient with a weapon you get no bonuses. If you're not proficient, you take a -4 to hit instead. Luckily, monks are proficient in every monk weapon, and your DM included the spiked chain in this number.