I'm so sorry to hear your dog is sick.
Though I agree antibiotics are a good first defence against stomach illnesses, the antibiotics themselves can also aggravate stomach acid and cause vomiting. It is a catch 22 at times. Seeing as he vomits, more so when the stomach is emptier (thus bile), and has done this at times in the mornings, it is likely he's got some acid reflux which needs attending to in order for this antibiotic to help any bacterial build up. It is often within 3-4 days you notice a difference with an antibiotic, but the antibiotic, like I stated, can add to the problem of vomiting as well.
Try giving some pepcid at a dose of 0.25mg per pound of body weight, as long as your dog has been fairly healthy otherwise (no liver/kidney disease or on heart medications). Then you can try very very small amounts of that bland food, like the boiled chicken or even baby food. Just about a tsp or so.
If he is able to hold down, try again in 2-3 hours this same amount. If doing ok, do this for a few hours, then about 1/2 a meal amount for his next meal time. You can repeat the pepcid in 12 hours as well, if you feel it is needed (while the bland diet helps the most, the pepcid may help speed along the GI's settling).
If doing ok, keep on bland diet for a couple of days, then gradually switch back to normal food. If not able to hold down even the pepcid, he'll need a vet exam sooner than later, as injectable medications will be called for, and further diagnostics may be needed to see if this is more than just a stomach upset. A different antibiotic may be needed, or bloodwork to see if other organs are involved causing this. Also, make sure he's drinking water or even some unflavored pedialyte the entire time so as not to dehydrate (small amounts at a time), and keep him indoors while recuperating, except for short leash walks only to do his business.
Here's some more info about Pepcid. If any concerns, it is always best to check with your vet before giving (you can certainly start the bland diet protocol and add Pepcid later if needed after speaking to your vet). It can be given with clavamox:
Best of luck, hope your dog is better in no time!