It may be known more broadly than just in Britain but I've not heard it in my neck of the US (Texas) and wouldn't immediately guess at the meaning of it.
A similar question came up a couple of years ago on our sister site English Language & Usage and it seems that there are native speakers around the world - Americans, British and Australian at least - who are unaware of this usage of "repeat".
From the answers and comments:
repeat 7. to cause a taste to return after eating, as through belching –TFD - I've never heard that one before. – Mazura Jan 27 '16 at 9:23
Likewise, northeast U.S. here, and I've never heard this usage before today. – Daniel R. Collins Jan 27 '16 at 16:06
Brit here, and I've never heard this usage either. – Rand al'Thor Jan 28 '16 at 20:30
However, there were a few Americans among the other British, New Zealanders, and Australians who had heard of it, though some noted that it was rare or only heard from an older audience:
I have heard this usage, northeast US. Primarily among older generation though. – Thronk Jan 29 '16 at 16:34
As an American, I've heard this before too, in more or less the same phrasing - but only in older written pieces. I had the sense that it was a non-American usage in general, though I would've assumed British. – recognizer Jan 27 '16 at 15:22
This is a small fraction of the anecdotes on that question, so I do encourage you to review more of it.
As to alternates if it's not used in the US, that's more difficult. Personally, I'd go the uncouth route and say something like:
- I've been burping the chili I had for lunch all afternoon.
- Every time I burp, I get the flavor of that curry again - and it's not a good thing.
- The flavor of those cucumbers keeps coming back [up].