Firstly, there is no need to vote for independence in order to protect the Scottish NHS from privatization or cuts - because it's already the Scottish Government's responsibility. As the IFS paper says:
Health is already a devolved matter - that is health policy and funding is the responsibility of the Scottish Government. This means the Scottish NHS does not have to make more use of private sector providers just because the English NHS is (and indeed, it hasn't't been).
Secondly, the figures suggest that if Scottish people want more money spent on the NHS they should vote for closer union with England rather than a break-up. Despite the Coalition government's austerity policies, which have meant that overall spending on the public sector has fallen by 13% in England, spending on the NHS has risen by 4% in real terms between 2009-10 and 2015-16.
Scotland, by contrast, chose to spend 1% less on the NHS.
Thirdly, if you were thinking the figures from the last few years were an aberration, think again! The IFS looked back to the period between 2002-3 and 2009-10 and found that "health spending per person grew by 29% in Scotland compared with a 43% increase across the UK as a whole."
What does this mean for the prospects of health spending in Scotland? Well, given planned spending cuts by the U.K. government over the next few years it is likely to become harder and harder to protect NHS spending in Scotland if it votes to stay in the union. However, the IFS also has a warning for the implications of a Yes vote (emphasis mine):
In the short term, then, it is hard to see how independence could allow Scotland to spend more on the NHS than would be possible within a Union where it will have significant tax raising powers and considerable say over spending priorities.