In the example where you're making your bicep as big as possible, "flex your bicep" is the most natural.

In the example where a child is jumping on your stomach, "tense" or your muscles is the most natural, and "tighten" is also good.

To "tense" or "tighten" a muscle means to engage it, usually for some mechanical purpose, like doing work or protecting your stomach from a child jumping on you.

To "flex a muscle", on the other hand, means to engage the muscle in order to display it well. If I flex my abs, the intent is to make my abs look good, like maybe when I'm on the beach or being photographed.

The colloquialism "to flex (on someone)" means to show your power to intimidate someone else. It comes directly from this meaning of "flex" for display.

In the example where you're making your bicep as big as possible, "flex your bicep" is the most natural.

In the example where a child is jumping on your stomach, "tense" or your muscles is the most natural, and "tighten" is also good.

To "tense" or "tighten" a muscle means to engage it, usually for some mechanical purpose. If I tense my abs, I might be protecting my stomach from a child jumping on me, or I might be doing a sit-up exercise.

To "flex a muscle", on the other hand, usually means to engage the muscle in order to display it well. If I flex my abs, the intent is to make my abs look good, like maybe when I'm on the beach or being photographed.

The colloquialism "to flex (on someone)" means to show your power to intimidate someone else. It comes directly from this meaning of "flex" for display.