It should not be a problem using Avios to get to DXB as long as you are a bit flexible on dates and:

i) do not travel to the middle east on a Saturday, Sunday or Monday
ii) do not travel from the middle east on a Tuesday, Wednesday or Thursday
iii) do not travel during the eid holidays or UK school holidays
iv) consider travelling via AUH instead.

For best use of Avios I recommend:

Step 1: consider a range of dates when you could travel
Step 2: within those dates see what is available out of all routes on the BA network
Step 3: choose a destination that is probably interesting and you may not have otherwise thought of, but has availability - for example, consider Asia or India instead of North America.