Inflation rates in Spain and Portugal during the 16th century

There isn't anything approaching annual time series data on these questions, so economic historians have to estimate them from other data.

Kugler and Bernholz estimate that Spanish inflation averaged 1.1-1.4% per annum in the 16th century. This may sound low by modern standards, but it was quite high considering that early modern economies generally exhibit very stable price levels. (Piketty talks about this extensively in the historical portions of "Capital in the 21st Century.")

Your question about the "amount of silver or gold possessed by the crown" may be better treated as a question about flows, not stocks. If the crown hoarded all the precious metals imported from America, it would have no effect on the monetary supply. But there's no doubt that the crowns acquired - and spent - prodigious amounts of "new" silver and gold in the 16th century. As Kugler and Bernholz show in Figure 1.1, the real increase in precious metal imports from the New World only begins to accelerate around the discovery of Potosi in 1545 (for a total of around 150,000 tons of silver). But then why did inflation characterize European economies from the very beginning of the 1500s? Central European silver output doubled at the beginning of the century, due both to new mining methods and the opening of new mines. Central European silver production declined sharply in the 1530s, but Potosi and the New World would more than make up for this slack within a decade.

Here's a nice graph showing consumer price inflation from 1300-1600:

And here's one looking at wheat prices in London only:

Just eyeballing these, inflation may have picked up in the early 1500s, but 1545 looks like the real discontinuity to me.