DLA isn't for a particular condition, it's for the care and mobility needs over and above those needed by their peers.
From www.gov.uk/disability-living-allowance-children/eligibility
"The child’s disability or health condition must mean at least one of the following apply:
They must have had these difficulties for at least 3 months and expect them to last for at least 6 months. If they’re terminally ill (that is, not expected to live more than 6 months), they do not need to have had these difficulties for 3 months."
These are a few things to think about if you want to proceed with the claim. I'm not trying to put you off, I'm just wondering how you are going to provide evidence for the 'much more looking after' criteria.
What you want is 1to1 weekly sessions with a SLT, yet practically, how much time would that extra care you say he needs add up to, 30 mins per week?
All they've done is come and assess him, and give us material to work at home. His preschool are involved and also given material
How much time do you spend at home daily or weekly on using the materials the SLT gave you?
Would you still use the at home practice if he had the weekly therapy you'd like?
Can you make a case that shows he needs "much more looking after" than his peers because of his speech delay?
How could you provide evidence that his speech difficulties are expected to last at least 6 months from when you apply?