How can I tie a note from one flow to the next?
You can’t, I’m afraid: flows are completely independent of each other, so you can’t join musical material between them in any way.
Mendelssohn, Violinconcerto E-Minor Op. 61 comes into my mind:
There is a bassoon note (a „b“) tied over from movement 1 to 2, connecting both movements. So they will have to be written in one flow…
For reference, this has implications similar to a question I asked weeks ago about creating cautionary time and key signatures at the ends of flows (for these exact situations). Daniel said that this was not implemented (and, I assume from his concise answer, not on the roadmap at this point). It’s a shame, since as you and Elaine Gould point out, it does come up.
Being able to merge two flows into one would mostly obviate this limitation, and is a more important missing feature - in my view.
At the moment, I need to change flows in order to apply different settings - not just because it’s a new movement. Possibly my current incompetence with Dorico.
I’m worried that Dorico’s philosophy for notation that is unusual is ‘that’s stupid, Dorico’s way is better and it’ll never be able to do that’. This is by no means a contemporary notation issue. Chopin often broke the rules for the sake of clarity.
I note that the Mendelssohn example has a regular double-barline and no page break. Also a new tempo mark but no movement numbers or titles. This whole concerto as written would definitely be one flow in Dorico.
Curious: what settings?
Cautionary Time and Key Signatures, for one thing. It can also be desirable to be able to use different spacing algorithms for different movements or even parts of a movement. This is one of Finale’s strengths: you can load different spacing libraries and apply them to different parts of a score. I use this often for multi-movement works, loading and applying a looser spacing algorithm to a slow movement with mostly 16ths and shorter note values, and a tighter algorithm to a fast movement with mostly 8ths and longer note values. I even use it for different parts in a score: looser for a violin part full of 16ths and tighter for a horn part full of whole notes. At the moment, I believe this is only possible in Dorico in different flows.
No, with a Note Spacing Change you can change the note spacing values at any rhythmic position within a flow.
To paraphrase Steve Jobs: “If we have to use Note Spacing Libraries, we screwed up.”
I strongly disagree. Read my post above. How is a program to know that you want a quarter note to be spaced differently because of some context only clear to an experienced musician?
I really agree! I’ve sometimes spaced a line differently because of the spacing of the system above it.
I’m engraving a piece that needs to tie between flows. It’s a suite of poems by different authors, so each new poem has a title, poet, and different scorings, moods, tempi, etc. Each piece is a discrete unit. However, a couple of the pieces have a held note between the pieces.
Normally, I would just use LV ties, but I can’t put those on a note that is already tied. How to make an ‘end tie’ on the front of the first note?
Faking a new flow would be considerably more difficult!
IIRC you can add an LV tie to the last note in the tie chain, as long as that note is in a different voice to the previous note in the tie chain. Try that…
Presume you mean ‘first note in the chain’. No: that doesn’t work. If I tie two notes in different voices, the LV still goes at the end.
I had it backwards - sorry - thought you meant the final note in the previous flow, not the first note in the current flow.
BUT
What’s to stop you putting an F semibreve with an LV tie in another voice on the downbeat of the second flow? Give it an LV tie, suppress playback and set it to the same Voice Column Index as the main (tied) note? You know it’s there; I know it’s there; the world is none the wiser 
Bingo. The following tie went a bit mad, presumably trying to avoid the LV tie even though it’s been moved in Engrave mode, but I think it’s workable.
Thanks