The thread title says it all really: I've heard that 8mm chain fits gypsies made for old 3/8 imperial size, just wondered how accurately? Likely to jam, or no problem?
5/16" is much closer to 8mm, 7.9375mm to be precise so that could work. Presumably you've got a 3/8" gypsy which seems to be incompatible with metric chain. Best bite the bullet and get a new gypsy.
Depends also on whether the chain is BBB, HT, G40/G43 or other. The critical dimension when fitting chain to a gypsy is the number of links per foot, The diameter of the metal in the link is very secondary.
I have a gypsy that fits perfectly 3/8 BBB and 5/16 G43.
You can measure the number of links/ft in both chains or just buy a 1-2' piece to test.
I had, used for 15 years, a gypsy marked 5/16th and used it with 8mm metric chain.
As mentioned its the number of links per length that is important, rather than the wire size. Imperial links tend to be longer than metric links. However, for obvious reasons, windlass makers try to have as few different gypsies as possible as they most sell to both metric and imperial markets - so many are very forgiving.
The safest answer is to take a length of chain to the gypsy, or vice versa, and try it.