I am using prowritingaid to edit my writing and it keeps flagging all adverbs. They have a post related to it here. Yet I feel like adverbs as transition such as finally, additionally can be useful to connect sentences and add fluidity. Need some advice.
They don't have to be.
Compare adverbs to calories: you gorge on pie and chocolate, you become fat. However, not eating results in starvation and death. Every once in a while you need an adverb.
The problem here is confiding trust in a computer. Computers are rocks with lightning trapped inside and, while exceptionally good at math, make no distinction between good and bad foods. They'll slap the 2 kCal head of lettuce from your hand and shout 'No! Bad! It ends in -ly so it must secretly be chocolate cake!'
Wrest control back from your computer. A sentence reads better with an adverb? Then ignore the red Twizzler drawn under it.
My understanding of the main objection to adverbs is that it dilutes the writing. Rather than saying "Jack ran very fast" one ought to write "Jack sprinted". Same idea, but the second version is punchier in that it takes less time to read. If you can find a stronger verb that can replace a weaker verb modified by an adverb, you should consider it. But your consideration should include notions about how the narrator typically expresses ideas, about how the sound of the language soothes or incites the reader, and about how the language sounds. It might be that "Jack ran very fast" becomes "Jack ran as if all the demons of hell were chasing him!" Not as punchy but maybe more effective in conveying the writer's ideas.
Since you mention transition, are you using adverbs such as "meanwhile", "later", "afterward" and the like, to move to a new time, new location or new set of characters? If so, consider instead leaving a blank line and then dropping clues in the next paragraph as to where or when you've changed to, without your having to call out the change with an adverb.
If not, then please be more specific about what kind of adverbs you're using that are getting flagged.