Dogs can get hiccups, but I've never seen a dog keep them for more than 15 minutes or so, though I guess it is possible. This sounds more like constant gulping. Excessive saliva and gulping and licking his mouth are signs of mouth pain, nausea or sometimes a seizure. Check your dog’s mouth for tartar on the teeth, possibly red gums, darkened teeth, broken teeth or something caught between the teeth or gums. If you find something stuck, try and remove it. If it is bad teeth, you can give him Buffered aspirin can be given to a dog with a dosage of up to 5 mg per pound every 12 hours. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet.
Check just under your dog’s jawbone for a swelling and under your dog’s tongue for a swelling. This is where some of your dog’s salivary glands are located. If you find a swelling here, it’s possible your dog has an accumulation of fluid near the salivary gland called a sialocele which is causing your dog to salivate more. This condition does require your dog to be seen as soon as possible. You can read about it here:
If you suspect it may be due to nausea you can try some Pepto-Bismol which can be given to a dog at 1 tsp per 5 pounds every 6 hours for upset stomach, gas, or diarrhea.
If it is possible that your dog ate something toxic such as chocolate, cocoa mulch, antifreeze, medications they will need to see a vet immediately.
You can read more about excessive salivation on the following website:
Hope this information is helpful to you.