My husband, who grew up speaking Polish at home, says it's pronounced niether pownchki nor poonchkey, but ponshky.
I think these variations might reflect regional accents.
As to how the spelling guides the pronunciation, Ari says he doesn't know.
But my mother's first husband was a linguist (and sinologist) at Magdaleine College, Oxford.
He said that every language that uses the European or Cyrillic alphabet uses it in a different way.
For instance, in Italian, vermicelli is pronounced vermichelli while zucchini is pronounced zukini.
The way each letter (or combination of letters) designates a specific sound is purely arbitrary.
Different languages use different vowels and consonants. So rather than inventing different symbols for each sound the tendency is that each language develops its own conventions for how to assign a sound to each of the pre-existing letters of the chosen alphabet.
English is the least predictable, the least phonetic in its spellings.
Consider the sound "oo": tooth, book, coordination - oo pronounced 3 different ways.
Consider the spellings: there, their, share, bear, air - five spellings for the same vowel sound.
Only two examples here, but irregularities dog every correct sentence.
We learn it by rote as small children and come to take it for granted; pity the poor foreigner who has to learn it as an adult.
The only consistent rendering of sounds is via the international phonetic alphabet.
To give an example, the various spellings for the "air" sound are all rendered as /ɛr/. This sound is named or referred to as a "schwa".
The schwa sound is a combination of an indefinite vowel halfway between a short "a" and a short "e".
The "air" sound is made with the addition of a slight r sound at the end.
One can see how complex human vocalisations are by looking at the IPA sound chart.
https://upload.wikimedia.org/wikipedia/commons/9/94/Extended_IPA_chart_2005.png
Even here, linguists will discuss with precise jargon exactly how various accents shift the basic sounds.
However you pronounce paczki, I hope you enjoy the flavour just as well. ;)
B.H.Wilson 
