How to remove tension from burl

If you take away some of the wood from the right side of the board as shown in the pic. Start a flat area in the middle as best you can. You will probably see it start to straighten out before you even make it to the ends.
You will loose some thickness but it's a fair trade.
Check moisture too
Good Luck

What are the present dimensions of the piece?

It's roughly 27"x12" and 1.25" thick

What do you plan on making with it?

I just need it flat for some epoxy molds. If not, and if the epoxy is t thick enough, it will make the board start to curl as well

If it wants to warp, there is nothing you can really do to stop it that doesn't risk other problems. Did it curl immediate during or after cutting or was it after it sat for a while? If immediately, then it may be tension but if it took some time (even as little as 15-30 minutes) then it is uneven drying. If laying it in the sun straightened it, then I think it is probably drying that is causing it so it may just need some time for the moisture to equalize. You will want to let it sit for a while and monitor the moisture content before you use it anyway. Make sure that you allow air to flow around both sides while you wait. Sticker it if flat or lean it against the wall.

It started to curl immediately after it was resawn, was pretty flat before that.

Burl isn't really wood like we think of wood. Its extremely irregular with stresses going any which way.

That said, most likely a moisture issue. Expanding on what Lazyman said, understand as wood dries the stress is released, to in every case of bowing or cupping, its as much a stress issue as a moisture issue.

You could try steaming it, but in the end I doubt anything will work other than "breaking its back" with release kerfs.

Good insight and kinda what I was thinking. Thanks!