Iron Palm Technique: You use your Constitution modifier instead of
your Strength modifier for determining damage with unarmed strikes.
Dragon Style: While using this style, you gain a +2 bonus on saving
throws against sleep effects, paralysis effects, and stunning effects.
You ignore difficult terrain when you charge, run, or withdraw. You
can also charge through squares that contain allies. Further, you can
add 1-1/2 times your Strength bonus on the damage roll for your first
unarmed strike on a given round.
There are two ways to interpret this: Munchkin RAW and Simplified RAW, since nothing says you cannot take both and use them at the same time.
Due to Iron Palm technique, you no longer have the option to use your Strength for damage. The wording is "You use", not "You may use". Thus, a monk with 14 Strength and 16 Constitution will deal +3 damage on all unarmed strikes.
By strict RAW, the same monk would then add 1-1/2 his Strength to his first unarmed attack. It specifies "add" not "use", so the monk would deal +6 damage with his first unarmed strike in the round, in addition to the other benefits of Dragon Style.
Since this enables stacking abilities for damage, I do not recommend this interpretation for munchkins. That said, it may be fine for new players new to playing Monk who need a slight boost.
Simplified RAW (Recommended)
One GM ruling: Iron Palm Technique replaces Strength with Constitution as your damage stat for all wording that identifies Strength as your damage stat.
With Dragon Style under this ruling, instead of 1-1/2 times your Strength on your first attack, you get 1-1/2 times your Constitution on your first attack. That same monk thus gets +4 damage on their first attack, just as if they had 16 Strength instead of Constitution.
I recommend this interpretation since it's a lot simpler than the Munchkin RAW interpretation and less open to abuse, though I am aware that the level of "abuse" possible or even required for Monk is up for debate.