No, you wouldn't get four attacks
Feral Combat Training does not allow you to make additional attacks during your furry of blows, it allows you to use natural weapons on your furry of blows:
Benefit: Choose one of your natural weapons. While using the selected natural weapon, you can apply the effects of feats that have Improved Unarmed Strike as a prerequisite.
Special: If you are a monk, you can use the selected natural weapon with your flurry of blows class feature.
This has been clarified on a FAQ entry:
Feral Combat Training: What does “with” in the Special line for this feat mean for monks making a flurry of blows?
Normally a monk who has natural attacks (such as a lizardfolk monk with claw attacks) cannot use those natural attacks as part of a flurry of blows (Core Rulebook 57). Feral Combat Training allows you to use the selected natural attack as if it were a monk weapon—you can use it as one of your flurry of blows attacks, use it to deploy special attacks that require you to use a monk weapon, apply the effects of the natural weapon (such as a poisonous bite) for each flurry of blows attack, and so on.
The feat does not allow you to make your normal flurry of blows attack sequence plus one or more natural attacks with the natural weapon. In other words, if you can flurry for four attacks per round, with this feat you still only make four attacks per round... but any number of those attacks may be with the selected natural weapon.
This doesn't change the number of attacks you can make, you simply replace an Unarmed Strike or Monk Weapon attack by a Natural Weapon attack. In other words, if you are allowed 2 attacks on your flurry of blows, you could replace any of them (or all of them) by the selected natural weapon, but you still will only make 2 attacks.
But you will get five attacks using them as secondary natural weapons
If you want to mix your unarmed/monk weapon attacks with your natural attacks, you will have to apply the penalties for using (secondary) natural weapons into your full attacks normally (-5 attack penalty and 1/2 str bonus on damage). A vanilla monk cannot mix natural weapons into their flurry of blows, but that restriction was removed on the Unchained Monk's Flurry of Blows, which simply grants an additional attack using unarmed/monk weapons.
In other words, you calculate your flurry of blows attack bonuses normally, then add your additional natural attacks at -5 penalty. So, if you attack normally with +5, those attacks are at +0. The damage from those attacks use only 1/2 your str bonus (str 18 would only apply +2 to damage), and Power Attack's damage bonus is also reduced by 50% (round down), since it deals reduced damage if using a light weapon or secondary natural attack.
This bonus to damage is halved (–50%) if you are making an attack with an off-hand weapon or secondary natural weapon.
Example, using the stats you gave us: BAB +2, plus +4 str, total +6 melee attack bonus. You have weapon focus (bite) and power attack (-1 attack). Note that the bear shaman does not list these natural attacks primary or secondary, so we can only assume they are all primary.
- A standard unarmed attack is done at +6 (1d6+4 damage);
- A standard claw attack is done at +5 (1d6+4 damage);
- And a standard bite attack is done at +7 (1d6+4 damage).
On a flurry of blows, you gain one additional attack, and all natural attacks not done using Feral Combat Training become secondary attacks, and as such you have the following options:
- Without Power Attack: Unarmed +6/Unarmed +6/Bite +2/Claw +1/Claw +1 causing 1d6+4/1d6+4/1d6+2/1d4+2/1d4+2 damage;
- With Power Attack: Unarmed +5/Unarmed +5/Bite +1/Claw +0/Claw +0 causing 1d6+6/1d6+6/1d6+3/1d4+3/1d4+3 damage;
You can replace the "Unarmed" with either your claw or bite attack, but then the attack bonus for bites will increase by +1, and the damage for claws will decrease to 1d4+4 or 1d4+6 with power attack.
Remember that each natural weapon can normally be used only once per attack sequence.
