Nobody likes paying taxes, especially when one disagrees what is done with them. But one can suspect that the more one identifies with the taxing state, the less one would want to evade taxes. While this hypothesis makes intuitively sense, the real question is whether this effect is economically relevant.
Kai A Konrad and Salmai Qari test this using data on the size of shadow economies and a measure of patriotism. You can rightfully argue that these two variables are very imperfectly measured, as they are based on polls. They also use an aggregate measure of the shadow economy, a notoriously difficult object to measure. When regressing patriotism on tax compliance, they include of course a series of controls, but miss the most important ones: the tax rate and penalties for non-compliance. There is plenty of evidence that tax compliance will depend on them. This can explain why the shadow economy is so small in the US: tax rates are low and penalties are unusually high. This makes you wonder whether the positive impact of national pride is really measuring what the author think it is. Arguably, the tax rate and penalty would be included in the country fixed effects, but this misses the actual marginal tax rate of the polled person, especially when taxes are more progressive. Also, one cannot exclude that patriotism is correlated with tax rates or tax penalties.
Economics has taught us that people respond to economic incentives, too bad that was forgotten in this study.