No, the two da's are a complete preposition (da). A is yet another preposition, but it's never used between qualcosa and an infinite verb.
The euphonic D can only be seen in ad (not da, that's a different preposition), ed (and), od (or). Of these, just ad is a preposition (a + d in case the word following a begins with the same vowel, otherwise it remains a). Roughly speaking, da and a are opposites: da means from, a means to.
To achieve a better sound, articles and nouns ending in the same vowel are contracted: la anatra = l'anatra (the duck), lo ostacolo = l'ostacolo (the obstacle); verbs and other words are often cut, especially in poetry, as in "E il naufragar m'è dolce in questo mare" (L'infinito by Giacomo Leopardi), the uncut verse being "E il naufragare mi è dolce in questo mare", or in Com'è andata a scuola?, "How was school?".
But this da doesn't belong to any of the above.
The English construction "something to [verb]" is always rendered as "qualcosa da [ verb in -are, -ere, -ire] in Italian. It's the way this saying works, and you could rewrite it like this:
Qualcosa da bere = qualcosa che può essere bevuto (something that can be drunk)
Qualcosa da mangiare = qualcosa che può essere mangiato (something that can be eaten)
Qualcosa da leggere = qualcosa che può essere letto (something that can be read)
The latter forms are very seldom used in the language, however both sentences have the same meaning.
A similar construction can be found in:
C'è da andare a prendere il latte. Andare wants an a in front of an infinite verb. C'è da can be translated as "There is to". A literal translation would be "There is to go to take the milk", meaning someone has to go buy some milk. The first to is translated with da, because it belongs to the "c'è da" construction, and the second to, being between andare and an infinite verb, is rendered as a.
Non c'è nulla da fare. There is nothing to do. [Non c'è nulla che può essere fatto]
Non c'è molto da fare. There is not much to do. [Non c'è molto che può essere fatto]
Cosa c'è da mangiare? What is there to eat? [What is there that can be eaten?]
Prendo il volo delle sei.
This is not an euphonic D either. Delle is a long preposition that is created by fusing together di + le (as if we were to join of + the in English). A rough English translation could be "I take the flight of six o' clock". Delle, in this case, refers to the departure time of the flight, meaning there is a specific flight that takes off at that time ["I take the flight that takes off at six"].
If you were to use alle sei, you would have to say Parto alle sei, "I leave at six". This sentence is more general, as it doesn't contain any specific information. Prendo il volo alle sei sounds a bit weird. You could use alle in this kind of situation:
A che ora hai il volo? What time are you leaving? [At what time do you have the flight?]
Ho il volo alle sei. I leave at six. [I have the flight at six]
Of course, you could also say Il volo che prendo parte alle sei [The flight that I take leaves at six]. Only when you're talking about a specific flight, or train, or bus drive at a specific time, you mark them with di:
Il treno Eurostar delle tre. The Eurostar train of three o' clock. [The Eurostar train that departs at three o' clock]
L'autobus delle due e mezza. The bus of half past two. [The bus that arrives at the bus stop at half past two]
Il volo Alitalia dell'una. The Alitalia flight of one o' clock. [di + la]
What may be confusing here is that the English to can be translated in many ways in Italian (either with di, da, per, a...). Italian prepositions are much unpredictable, and this is why it's a good thing to memorize, along with each verb or saying, the prepositions that are used.
Hope this helps!