It is okay to use slugs in either improved cylinder, or modified chokes. I don't recommend shooting slugs with a full choke, neither will any manufacturer.
I have used slugs in both chokes with a browning semi with no problem. If you are ever in doubt though, you should contact browning arms. Here is the info from their site. Frequently Asked Questions--Can I shoot Remington® HEVI-SHOT® in my Browning shotgun?
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