S, if they are truly choking, a slap on the back isn't likely to help much.
True choking is silent. There is no noise as there is NO air getting in or out. Gagging is usually somewhat noisy... coughing and retching like sounds, sometimes mixed with short spaces of silence.
If they choke, you are supposed to get them out of their chair, lay their chest on your forearm, with their head at your hand. Lower their head so their bum is more in the air than their head, then use the heel of your hand to bang on their back, in the middle below the shoulder blades, near where the diaphram is. You might have to do this a couple of times and pretty hard, but it should help.
Never ever stick your finger in their mouth if they are choking! I can actually push the food back further into their windpipe and make the situation much worse.
Offering complex foods is always scary, I think. We worry so much about their ability to handle it. What BLW has taught me, though, is that if you don't help them, they tend not to do things they aren't ready for. So, I just put the food in front of him ("offer") and leave him to it. I don't show him or encourage him. The only thing I do is eat with him, so he can copy how I eat. If he is capable of picking the food up and getting it to his mouth, he rarely has trouble with it. He gags sometimes, but is gagging less and less all the time.
And he has eaten LOADS of crazy stuff... from whole baked potatoes, to all kinds of fruits and veggies... sandwiches (his favorite is a roast beef sandwhich)... chicken... tacos... steak... tuna sandwiches... tuna on crackers.... cheeses... chinese noodles... pot roast... beef stew... grilled cheese sandwiches... peanut butter and jelly...
Basically anything that I have eaten!
It is scary at first, no doubt, but they are better at this sort of thing than you would think.