A 'flexible' Cash ISA lets you withdraw money and replace it within the same tax year without using more of your annual £20,000 allowance. Standard (non-flexible) ISAs treat any withdrawal as permanent - if you put £10,000 in then withdraw £3,000, you've still used £10,000 of your allowance and can only contribute another £10,000 that year.
With a flexible ISA, the same withdrawal frees up £3,000 of headroom that you can replace before April. For an emergency fund parked in an ISA this is the difference between 'usable savings' and 'savings I'll only touch as a last resort'. Trading 212, Chip and Tembo all currently offer flexible Cash ISAs. Atom Bank and the building-society fixed-rate accounts typically do not.
If the wrapper is going to hold money that might genuinely need to come out and go back in (e.g. tax-bill cash sitting between January self-assessment and April), insist on flexibility. The rate difference vs a non-flexible alternative is usually irrelevant compared to the allowance you'd otherwise burn.