δώσειν is the future infinitive here with ὑπέσχετο since verbs meaning "promise" can take a future infinitive. προεῖπαι must go with the earlier ἔπεμπον (sent messengers to tell beforehand/warn) and ὅτι goes with προεῖπαι.
But it's the ὡς that I can't really explain, and I find it a really tricky word at times. The meaning seems clear, but one possibility is that this is case where a verb has been ellipted and usually that verb is taken to be ἴσθι so it's "know that they..." to make the statement stronger. That's how I read it here in context, as strengthening that they will find a way to escape.
So overall I read it as
[sent messengers to blame..] and at the same time to remind [them] of however many [=what] the Persian had promised to give them if they change sides [< participle μεταβαλοῦσι], and to tell them that if they didn't aid the Athenians, they themselves would find some escape.