Earlier quoted context omitted.
A flat tax on income would help, but it's still a tax on income, and so you can move that around with clever transfer pricing etc. Land value tax works even better: it's physically impossible to move or hide land.
Flat tax is not just about removing thresholds, but also using the same tax rate across the board. If you tax in the same way income, capital gains or corporate profits, don't give a tax exemption for debt, don't charge a stamp duty on property (or charge the same rate on the purchase of all assets, property or not), etc, then you kill all these tax schemes.
Yes, it's a good idea to put eg debt and equity on the same level; don't tax transactions that improve economic efficiency (tax consumption instead for example).
Land value tax is still a great idea for these and other reasons. Eg you can jack the lvt really high and basically tax away all land rent without negatively impacting the economy. So even in an otherwise 'flat tax world' like you describe, it might be a good idea to get the majority of revenue from taxing land rent (and in the wider sense, resource extraction and commons like pollution carrying capacity).