When a choke is properly applied, no amount of "neck flexing" will save you.
Let's use a rear naked choke for example. The attacker is behind the victim. The choking arm forms a 'V' shape at the front of the neck with the elbow pointing down. This is to target the carotid arteries. Closing one of the arteries will not completely stop blood flow to the brain. A person may feel slightly light headed, and vision darkened, but only closing one will not put them to sleep. To close both arteries, the choker applies the forearm to one side of the neck, and bicep to the other side. The choking arm grabs the off hand bicep, and the off arm comes behind the head for further force the opponent's neck into the choke. Closing both arteries, for around 5-8 seconds, cuts off blood flow to the brain, and the person being choked will go unconscious. No neck tendon, muscle, or anything else is strong enough to withstand the squeeze needed to close the arteries.
Now let's use an arm triangle choke. The same principle applies, closing both arteries. The difference here is the choker uses the victims own arm to close off the other half of the choke. From the side of the victim, the chokers arm is wrapped around the neck from the front, with the opponents close side arm raised up next to their head. In this case the chokers arm is closing the far side artery, and the victims own shoulder is closing the close side artery. No amount of neck flexing can stop this when properly applied.
What you most likely ran into was improperly applied chokes. It's amazing how difficult it is for a beginner to actually choke someone unconscious. I've had newer folk full on squeeze my neck for as long as they want, with no results. No flexing or anything special on my end. They just can't hit the arteries properly (bad technique), or for long enough (their arms burn out). Another thing you likely ran into is choking technique changes for different neck sizes. Your training partner may have not been used to choking a neck as small as yours.