As I'm sure you're aware fro your question, amoxycillin is a prescription drug and should only be used under the supervision of an examining veterinary surgeon. This is to make sure that the correct drug is prescribed for the problem, that there are no other problems present and to control any possible side effects or resistance.
A vet exam would also be recommended in your dog's case as the symptoms of tracheitis can be similar to the signs of having a foreign body in the throat etc. Amoxycillin is okay as an antibitoic, but it does have a limit as to the tyoe of bacteria that it can kill, and also the tissues of the body that it penetrates. This drug is not the best choice of antibiotic for the throat - you would be better with amosycillin-clavulanate or oxytetracycline.
If you are absolutely unable to get to a vet, then you can try the tablets, but be aware that you are giving them at your own risk and that this is not advised.
I have enclosed a link to a page that give some more information about the drug.
The range of dosing is quite large - 5-12mg per lb of dog - I would go for 8-10mg/lb twice daily, which is about one third of a tablet. If there is not any improvement after a five day course, then you really need a vet.
As I have said - try it and see. If there is no change you haven't lost anything. But as vets online we are just obliged to warn you of possible complications of giving meds at home, that's all. We have to make sure that people are aware of the prescribing laws - you would be suprised at what some peopole suggest administering to their dogs at home, so we have to be cautious about this.
I hope it works for you!