Printing money to put into a Superannuation or UBI fund It is fiscal policy to keep inflation at between 1-2% (in New Zealand at least) 
Various tools are used to keep inflation in this range.

Let's say the average inflation rate is 1.25%

What would happen if a small country (this probably would not work if the US tried it) printed* enough money to push inflation to 2%. Then put that money into a global index fund (and gold as a hedge).

This fund would be earmarked for superannuation, Universal Basic Income (UBI),  'a rainy day', quantative easing during a depression, etc.

In say 50 years the fund could become quite substantial. It could then be used to offset (all?)taxes with the fund's dividends. 

What is the obvious flaw in this plan of printing money to finance a long term government fund?

*Not literally print, but you know what I mean.
Here is an interesting article on the link between helicopter money (“printing money”) and UBI:
Helicopter Money and Basic Income: Friends or Foes?
First, helicopter money (or funding a SWF) is arguably a more straightforward way than QE (asset purchases) to increase inflation to the target:

Instead of QE, the ECB could start a helicopter money scheme by giving
200 euros per adult citizen for one year – no strings attached, no
taxes involved, simply courtesy of the ECB’s (digital) printing
presses. This would involve about one-third of the money printing of
that under QE and yet would be more likely to fulfil the ECB’s
objective. … The ECB’s temporary scheme would allow some time for EU
policymakers to create the institutional and fiscal infrastructure for
such a eurodividend to be functional.

Instead of paying a UBI directly to citizens, or fostering economic activity by buying government debt like in QE, the central bank could also use newly created money to set up SWF to make consistent UBI payments over time.
The UCL IIPP is proposing the wider use of SWF:
Public wealth funds: Supporting economic recovery and sustainable growth
November 2020

Previous pandemics have, according to some studies, depressed growth
for decades (Jordà, Singh and Taylor 2020). One explanation of this is
that state-backed loans given out during the pandemic build a
corporate debt mountain that stifles many companies’ growth for years
to come. ... Under such conditions, public sector equity investments
or debt-for-equity swaps become an attractive option. By taking stakes
in threatened, strategically important firms, governments can not only
maintain jobs and provide a financial cushion to allow for firms to
recover and invest, but also ensure the taxpayer earns some reward
when the economy does emerge on the other side.

While you would likely want to use public leverage to impact investment towards public policy objectives you would arguably not want to end up with the government actively managing the economy.
The most neutral investment would be for the government to invest in land given that who owns land does not affect supply, which is fixed, or in practical terms governed by public planning laws.