Should Buddhists avoid Amazon and Starbucks out of concerns about tax avoidance?

If you want to do so as an act of protest against their practices that's a good thing in my view but I don't think you can make it mandatory. It seems to be a general principle in Buddhism (at least in the Theravada school) that an act isn't intrinsically evil unless it involves harm in terms of clearly evident causation rather than in terms of indirect contribution.

Buddhism exists because it gained government patronage. It isn't a system for liberation from the government and it's taxes. Thats relatively recent ideology.

Actions of a Bodhisattva in High Places "Good man, if a Bodhisattva has achieved command, becoming the ruler of a great nation, he should treat every one of his subjects like an only son. He should teach them to discard evils and do good dharmas. He may have an evildoer rebuked and beaten, but will not take his life. He levies one sixth of people’s wealth as taxes."

And in the minor precepts:

(21) If an upāsaka who has accepted this precept fails to pay taxes for his business and runs away, he has committed the sin of negligence. Without rising above this impure act, which is conducive to continuing his cyclic existence, [after death] he cannot avoid going down an evil life-path.

Both quotes from the Upāsaka's Precepts, which is sort of precepts for non-renunciates.

So not only does Chinese Buddhism support the of paying taxes, it supports a tax rate of 16%

The precepts are written at a pretty high level, so I'm going to say that they are written to be read as rules to be followed in principle, not as rules that you can carefully nitpick.

http://www.sutrasmantras.info/sutra33c.html

From a Buddhist perspective is there any problem with this? The companies are not stealing nor are they breaking any laws - tax avoidance is perfectly legal as opposed to evasion which is not.

It's difficult to say why they avoid paying taxes. We cannot know the exact reason so this is based purely on theory.

The most obvious reason for why they are avoiding taxes would be because they want to maximize profit. If that is the case one could argue that their actions are based on the unwholesome root of Greed. In this case they are creating unwholesome kamma for themselves.

It could also be that they want to earn as much money as possible so that they can give as much money as possible to charity.

Should Buddhists avoid Amazon and Starbucks out of concerns about tax avoidance?

It depends on one's intention. If one's intention is to contribute to he upkeeping of tax avoiding companies so that they can earn more money then one should probably avoid buying at those companies since it will create unwholesome kamma for oneself.

If one's intention simply is to buy a cop of coffee then no problem.

One can also view it from the perspective of the company, i.e. from the perspective of the people who are doing the tax avoiding and thereby creating unwholesome kamma for themselves. One could minimize their ability to create unwholesome kamma for themselves by choosing to not buy from these companies. If more people choose not to support them it might end up in them choosing more carefully how they conduct their business.

There are probably many more perspectives than i mention here. These are just the ones that were most important for me to mention. Again this is purely theory since we do not know the reason behind tax avoiding. It could simply be that they need the money to open up another office building so that more people will be able to get a job.

I think the answer is No. You can, but due to your personal views and believes, it has nothing to do with Buddhism, from a Buddhist's perspective you should take care of your actions, they will receive the results of their kamma (if any). Focus on what you do and left undone as the Buddha taught.

Another thing is that these days almost 99% of the companies do some kind of tax planning that involves similar practices, you just don't know it.

In an extreme example imagine if someone says: I will not pay taxes because the government is corrupt, that is wrong, as a citizen you should pay taxes and the politicians will face, sooner or later, the consequences of their actions.