Is your flat small? would be A bheil am flat agad beag?
The sentence of this exercise – a bheil flat beag agad? means literally is a small flat at-you?, it has its subject – flat beag a small flat as single phrase, and a predicate agad at you. And saying that X is at Y is the Gaelic way to state that Y has X, so this is exactly do you have a small flat? and nothing else. It’s asking somebody whether they have a small flat (whether a small flat is at them).
On the other hand, when asking is your flat small? you know already that the person asked have some flat and you ask about its attributes – the subject is your flat, am flat agad in Gaelic – a concrete definite flat. And the predicate you ask for is small, beag, hence the Gaelic question: a bheil am flat agad beag? is your flat small?
do your causes lenition, so I think it would need to be do fhlat.
Also I don’t think one would use inalienable possession here and still rather say am flat agad for your flat – but then since my house can be both mo thaigh and an taigh agam, maybe do fhlat would also be used? see 184.108.40.206 Possession in Scottish Gaelic, 2nd edition by William Lamb – and there are at least a few Gaelic results for mo fhlat and do fhlat on Google.