Flood was cleared of a broken toe after England's 16-15 defeat to South Africa but he is expected to be ruled out of next Saturday's clash with New Zealand.
Burns was joined in the England camp today by Bath wing Tom Biggs, who received his first senior call-up after Ugo Monye suffered a calf injury.
Gloucester prop Nick Wood also linked up with England to act as precautionary cover for Alex Corbisiero.
The England medics are being cautious over Corbisiero, who played against South Africa but is only three matches into his comeback from a knee injury.
England coach Stuart Lancaster said: "Tom is next in line from the Saxons and we are looking forward to getting a look at him.
"Freddie has been in for two of the last three weeks (as injury cover for Jordan Turner-Hall) so we know what he can bring and Nick Wood will provide cover as we manage Alex's knee at the start of the week.
"Toby Flood's toe has been re-examined and there is no bone broken but we will need to see how it settles down over the next 24 hours."
Burns, 22, could go straight into England's 23-man squad to face New Zealand next Saturday.
Owen Farrell replaced Flood in the second half at Twickenham yesterday and would be England's likely starting fly-half against the world champions.
Burns is the leading points scorer in the Aviva Premiership this season and kicked five penalties and two conversions in Gloucester's 29-3 Aviva Premiership victory over Sale yesterday.
Anthony Allen did not link up with England today, remaining at home following his withdrawal from Leicester's Premiership defeat at Wasps due to illness.