The connexion of Seraphim ("celestial beings with six wings and human hands and voice") with saraph ("snake, flying snake") is possible, but posits that Seraphim were originally conceived of as having serpents' bodies (perhaps identical with the flying snakes of Isaiah, XIV 29 & XXX 6 -- esp. if you take these as largish dragons; but see below).  Possible, of course (Watson, if you're reading this: perhaps this also a more pleasing image than a chubby faced child...), but who really knows?  The problem is that the Seraphim aren't described as having serpents' bodies in Isaiah VI; nor do the Mesopotamian or Egpytian comparanda point in that direction.  If all the bits and pieces added up to a unitary image, it would be one thing; but Sharrap/bu as an epithet of Nergal is (I think) meaningless for us, and the  Egyptian creatures of a similar name are apparently more griffin-like...  So there's no real need to suppose that Seraphim, "celestial beings" and saraph, "snake" belong together etymologically. 
     It remains possible that we're dealing with two entirely different roots in Hebrew.  To make matters worse, as Seraphim are never attested in the singular, we don't actually know what the first vowel of the word was: any vowel in that position would have been reduced to schwa (which appears as "e" in our conventional transliterations into English).  It might (or might not) make a difference. 
     Whether or not either word can be connected to the verb *srp, "to burn," is again an open question.  The connexion turns entirely on the "burning" pain caused by a snake's poison (not exactly confidence-inspiring evidence).  The second Isaiah-passage cited below does refer to the "fiery, flying serpent" -- but the word "fiery" could already be an etymological play on Isaiah's part and need not be any genuine evidence for the connexion of saraph, "snake," with *srp, "to burn." 
     Finally, I'd personally take the "flying snakes" of Isaiah XIV 29 & XXX 6 as identical with the flying snakes mentioned in roughly the same region by Herodotus, II 75 -- as a creature small enough to be attacked and eaten by an Ibis -- and separate them from the Seraphim altogether; but that's just my opinion. 
     Isn't etymology wonderful?  Sorry, I couldn't resist this one...

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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.