ILR is indefinite if you stay settled in the UK. If he moves to the US for more than two years, he can lose his right to ILR.
It's perfectly fine to leave the UK whilst he's on FLR -- he just can't settle elsewhere. If he's planning on spending a substantial amount of time out of the UK whilst on FLR, that may affect his ILR application, but that won't be a problem if you're just planning to go on family holidays, etc.