Generally speaking, you want to do the fill coats within a day of glassing so that you get good chemical bonding.  If you wait longer, the epoxy is fully cured and you should sand the surface so the fill coats will have something to physically bond to.

I have used stain on a couple of kayaks but never on the coaming lip.  If you have not already, read this tutorial by Nick Schade:  https://www.clcboats.com/shoptips/finishing-tips/staining-your-kayak.html

The biggest deal is that epoxy will block stain from penetrating into the wood, so any staining must be done prior to gluing things together  Staining the coaming spacers will be a waste because except for the edges, they will be completly covered by the lip.  Any stain on the edges will likely be removed when you sand the spacer assembly smooth.  You may be able to stain the lip after assembly if you make sure there is no epoxy on top.

Another thing to keep in mind is that the coaming lip is a high wear area. Hands, legs, feet, spray skirts, paddles, etc. will all be rubbing, bumping and banging it. If you don't want the thin stained layer of wood possibly worn away, you may want to cover it with a light layer of glass (4 oz or less) for abrasion protection.

If you are going to be doing all that staining, the sanding and epoxy and glass application will be finicky. I really recommend that you use that procedure where the coaming is built on a polyethylene layer on the deck so that it can be removed for sanding and further processing before being permanently glued on. It'll give you much better access, let you remove all the epoxy so that the stain will penetrate and keep you from marring your deck.

BTW, the link to the stains in the Shop Tip is dead. It points to the discontinued  Behlen Solar Lux product and ends up on a blank page. The actual current Mohawk product is here.

Finally, remember if your staining experiment runs into some snags, you can always paint the coaming to be a contrasting color.

Laszlo