I agree that PDB should try Burns with Vlasic (or Dillon). However, I dug up the 5x5 numbers for last year and the GF%age weren't good for any D-men on the team now. Here's what I found (copied from another thread):
Last year, Burns CF% with Vlasic (370:44 TOI) was 54.1 but his GF% was 42.3. With Dillon (285:20 TOI), it was 54.8 CF% vs 40.0 GF%. With Mueller (264:56 TOI), it was 52.2 vs 44.0. This season with Vlasic his CF% is 54.5 while his GF% is 100 but there are only 59:17 minutes. With Dillon, his CF% is also 54.5 but his GF% is 27.3 with 111:17 TOI. With Martin, CF% is 42.0 but GF% is 39.4 with 446:52 minutes. He's only played 10 minutes with Mueller and has a 50.0 CF% and 0.0 GF% but that is a tiny sample size so I'd go with last season's.
The CF%ages are decent for everyone but Martin but the GF%ages aren't except for with Vlasic this season but that's a small sample size. It's worth a try but I wouldn't count on any D-man on the current roster playing well with Burns. Per last year, they may as well bring Mueller up and pair him with Burns.