"more flavours" is a correct and usable phrase in written English.
You can use it when describing a variety of options, such as "This store has more flavours of ice cream than any other place in town!".
Dr Pepper has way more flavours.
For better or worse, America is going to keep on adding more flavours to the melting pot.
A decade ago there were more flavours of condom in Iran than in London, New York or Paris.
Now I've nothing against "Moneymaker", especially if they are left to ripen on the vine for full redness, but I was looking forward to a salad comprising rather more flavours.
If you were willing (and able) to pay about $1 per scoop in convertible pesos, you could try more flavours and find gratification in an instant, but that would be missing the point.
The combined forces of Labour and Liberal Democrats would still be outnumbered by the Tories, and the prospect of a deal spanning Labour, Lib Dem, SNP, Plaid Cymru and one or more flavours of Northern Ireland MP lacks credibility.
