This one is prettier a flower than a rose.
Or am I not allowed to invert it and have to say
This one is a prettier flower than a rose.
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*This one is prettier a flower than a rose.
This inversion is not grammatical or idiomatic.
Ordinarily—let's say in 999 cases out of 1000—determiners (Det) precede modifiers (Mod).
... Deta Modprettier flower ...
In fact, one widely accepted analysis of noun phrases (NP) understands the determiner as a complement not to the noun but to the 'nominal' phrase (Nom) composed of the noun and its dependent modifiers, like this:
About the only situation I can think of where an adjective is permitted to precede a determiner is
a comparative construction when the adjective is embedded in another a comparative construction.1 In this example I've put the 'inside' comparative operators in boldface and the 'outside' comparative operators in bold italics:
This is so much prettier a flower than a rose that I will never grow roses again.
This construction is acceptable in any register. Note, however, that there is a slightly more formal variant which eliminates the unusual Mod-Det-Noun sequence by postposing the modifying phrase—moving it to the right of the noun. (This is standard with any modifying phrase which has one or more constituents to the right of its own head.)
This is a flower so much prettier than a rose that I will never grow roses again.
"If an adjective is being modified by a deictic degree adverb such as so, too, as, this or that then the adjective and adverb must go before, not after, the indefinite article." - that's for "prettier a flower" explanation. Now you know what should be up front. Source: When articles are placed after adjectives?
As for inversion - you have to start over :) as in your sentence there is no inverted word order. There is though in Araucaria's.