With all due respect, DonDriver, I would hesitate to offer that piece of advice with such confidence. Perhaps humor is not the style to which panda44721 aspires. That is not to say that humor is insignificant in the realm of magic; there are a great many successful comedy performers. If this is the way that he wants to do it, that is fantastic advice. However, if that is not a style that he wishes to pursue, or if comedy does not come naturally to him, the routine would fall flat.
After having seen five or six live straight jacket escapes, I have come to a somewhat disappointing conclusion: the performers who want to make the escape serious never commit enough to the necessary role of a struggling human being. If a person is bound in a straight jacket, that is supposed to mean that he is completely physically incapacitated with no chance of escape without assistance. This is the central focus of the escape! Some magicians make the effect into a message: "I am a magician, therefore I can easily escape from this straight jacket." That doesn't work very well, because it is more of a boast than an appreciable feat. Whether or not the jacket is actually easy to escape from is completely irrelevant. You, panda44721, as the performer, must make it appear to be the most difficult thing in the world to defeat! Part of being a magician is being able to create an illusion, and so you must create the illusion that this jacket is just as hard to remove as it should be. Remember, the straight jacket was invented to be inescapable, and that is what people expect it to be if they are to consider the escape impressive. So play the part!
Houdini used to do a straight jacket escape for which he had to dislocate his shoulder. That is one edited of a painful process, and it could be heard by the audience when he slammed his shoulder into the stage floor, and when the shoulder loudly popped out of its socket. Now, for all we know, this could have all been showmanship! So much of Houdini's reputation relies on eye witness accounts of things that people believed he'd done. Many things that he is famous for are things that he never actually did in the same manner as they were said to have been done. Houdini was the showman in magic. He knew how to make things incredible by "dressing up" whatever he intended to do. He could open a lock in ten seconds, but he would take three to five minutes slamming himself into the walls of his spirit cabinet or creating drawn out silences to make the audience wonder if this would be the occasion on which he failed to escape his bindings. Without the risk of failure, the act would fall flat.
The message here is that you don't need to add anything. All you really need to do is create the impression that this is a difficult thing to do. Adding chains would be a fantastic idea, though, because it raises the stakes in exactly that way. Consider other ways to dress up the illusion. Have a few people come up to the stage to examine the jacket's buckles and straps to ensure that they haven't been tampered with in any way. Let them search your sleeves and pockets for tools that would aid you in escaping. Tie yourself up with ropes. All of these things add nothing to the difficulty, but they create a convincing illusion, and that helps you to give a stronger performance. Most importantly, though, you must remember to struggle against these bindings with all your energy if you want a dramatic show of escapology! What would it look like if this jacket really was inescapable? Would you sweat trying to jerk your arms around? Would you grunt in frustration? Would your breathing become short and labored? What would your face communicate to the audience? Would you request that somebody help you by providing water while you take a two second rest after each step of progress? Ask yourself these questions, and answer them with realistic choreography.
On a final note, do not forget that there is a fine temporal line between rapt attention and boredom. If the escape takes three seconds, people will be unaffected. If it takes ten minutes, they will lose interest and become bored. The proper length of time will only become apparent to you through repeated performance. So pay specific attention to how long they stay poised at the edge of their seats. Make them fear for your safety or success, and I guarantee that amount of time will increase. If they fear that you won't succeed, or that you may pass out, they will be paying undivided attention to you. Don't let them expect that you'll be able to do it, and don't let them sit there with nothing to watch either.