Let's say, we have there 1st level Monk, and he has STR 17/+3. Now we are calculating base attack with his Flurry of Blows. For first level, we have "Flurry of Blows Attack Bonus" -1/-1, plus 1st level it is 0/0 and plus strength modifier it is +3/+3. When we are attacking with combination of Siangham, it doesn't matter, because it is still +3/+3, And damage is 1d6+3/1d6+3. Is it calculated correctly, or am i wrong somewhere?
Flurry of Blows Attack Bonus as Phill's answer, but damage includes the full Strength bonus.
A monk applies his full Strength bonus to his damage rolls for all successful attacks made with flurry of blows, whether the attacks are made with an off-hand or with a weapon wielded in both hands.
You do not add the monk BAB to Flurry of Blows, it has its own independent BAB, which the Str modifier is added to, ergo +2/+2. If the monk has levels in another class, you would add that BAB to the rolls.
Flurry of blows starts with -2/-2 because it's a combat move where you in theory use two weapons. So you get the -2/-2 attack penalty.
Then you add the BAB to your attack rolls from your different classes. The BAB for your monk class is special in the case of flurry of blows, it is equal to your monk class level and not the regular BAB for the monk's class level. So for a lvl 3 fighter / lvl 2 monk, you add +3 for the fighter BAB and + 2 for your monk BAB. In this example, you add +5 and the result is +3/+3.
Then you add your strength modifier, in the example of 17 Str it's 3. So the attack bonus becomes +6/+6. Furthermore, a monk never has offhand attacks (except when he is foolish enough to carry two one-handed weapons that don't count as unarmed strikes or monk weapons) so the damage bonus from your strength is added to both attacks.
A first level monk has no +1 BAB to begin with, but even then the flurry of blows uses a different, separate progression, which is to be summed to any other BAB from different classes.
For first level, we have "Flurry of Blows Attack Bonus" -1/-1, plus strength modifier it is +2/+2. When we are attacking with combination of Siangham, it doesn't matter, because it is still +2/+2, and damage is 1d6+3/1d6+3.