OK - I've heard one too many times about how the TRX rubs against your arms during the chest press.
If you find the strap is rubbing against your arms you can do one of two things:
1) Simply elevate your hands until the TRX is slightly above your arms.
2) To use a lower hand position, drop your elbows and slightly externally rotate your arms
Using either of these techniques will enable you to do the chest press without any friction at all.
If you've applied these two techniques and still the TRX is rubbing against you then perhaps... just perhaps, you are not as strong as you think. The primary reason for rubbing is that a user will choose an angle that is too steep for their ability so the body seeks another way to stabilize the action. Pulling the straps into your body provides that stablity but at a cost - Rubbing. This is especially true with strong, heavier individuals who have been training using a traditional approach and often lack the requisite stability.
So - Check your ego and move your feet!
Think of it this way - I can't bench press 300 lbs. If I'm dumb enough to load the bar up with 3 plates a side and then get stuck underneath it, is it the bar's problem or mine?
In this way you can get a super challenging chest workout that is
easily tailored to your ability and offers a way to integrate a number
of interesting set arrangments like drop sets and giant sets that can
be more cumbersome using other methods.