In Season 5
Deke is revealed to be the grandson of Fitz and Simmons.
Was there any evidence to support this other than he heard
using a phrase his mother used to use.
Did they ever do a DNA test or anything else to prove it?
In Episode 12 "The Real Deal", General Hale is investigating at the police station where Deke was. They swabbed the cell and Hale's assistant (Candice Lee) says that Deke does not match any one DNA profile Hyrda has, but does match two, Fitz and Simmons.
[Hale:] You got something?
[Lee:] I don't know. Thinking Deke Shaw could possibly be an LMD, I ran a genetic profile to see if he was biologically linked to anyone.
[Hale:] And it came up with a match?
[Lee:] No. It came up with two.
Agents of S.H.I.E.L.D., Season 5 Episode 12, "The Real Deal"
You can watch the scene here (starts at 19 seconds).