The way you arranged the adjectives and adverbs works perfectly; you achieved the exact, quite subtle meaning you intended. The "extremely hot, flowing flames" seems to catch the meaning you intend: that the flames flow because of the heat.
Ephraim N.
asked 08/23/19Is there any hard and fast rule for placing a coordinate adjective that is modified by an adverb first in a set or series of such adjectives?
For example, I want to describe a special type of fire. I could say, "Extremely hot, flowing yellowish-green flames began to come off of the wood," or I could say, "Flowing, extremely hot yellowish-green flames began to come off of the wood." The former obviously sounds much better due to the adverb hanging in between in the latter, and I am aware that "flowing," in this case, could serve as a cumulative adjective; however, in this special instance, I am describing the flames as "extremely hot and flowing" or "so extremely hot that it flows like liquid." The flowing nature of the flames is due to the high amount of pure heat, so I am NOT describing "flowing flames that are extremely hot." I am describing "extremely hot, FLOWING flames."
3 Answers By Expert Tutors

Brent W. answered 08/23/19
Teacher of English Literature and Writing
For your purposes, placing the cumulative adjective (the word, "flowing") at the beginning of the sentence to describe the flames is used as personification, giving the sentence more of an active voice. Placing the word "flowing" later in the sentence sounds more passive as the connotation here refers more to the direction or momentum building in the extremity of the flames.
Both examples are proper grammar uses, but it depends on the connotation you wish to bring to the noun "flames" to present its image without the need of simile and possibly without the need of metaphor. As a reader, I find the sentence starting with "Flowing," creates a stronger image and description that animates the flames as they are a natural, living element. It makes more sense then to personify and describe the "flames" using the word "Flowing" at the beginning of the sentence.
Ephraim N.
Ah, I see. I shall certainly consider what you have taught me this day. Thank you for your input. It is much appreciated. Oh, and thanks a bunch for confirming the grammatical correctness of it.08/24/19

Joel K. answered 09/01/19
M.A. in English with 7+ Years of Tutoring Experience
You may want to abstain from using the adjective “hot” to describe “flames,” since “flames” already contains the image of heat, for fire is hot. Adding “hot” is therefore redundant: the adjective functions only as a sound. Yet the sound of “hot” does not add all that much to the rhythm or rhyme of the sentence, and if it does not add, then it subtracts, making the sentence “weaker”—less impactful, less sublime, less poetic. But let me say that I love your creativity and intelligence: you are on fire.
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Ephraim N.
Marvelous! (I see what you did there!) That was astoundingly clever. Took me a bit to catch on to it. Thanks a bunch for your time and for letting me know that it's okay to have a coordinate adjective modified by an adverb after a preceding coordinate adjective. Just you using it alone is word enough for me.08/24/19