The Blue Square North club, who Burnley played in a pre-season friendly in August last year, took first year professionals Alex Coleman and Adam Evans on loan earlier in the season and have now opted to sign two of the youth team until the end of the season.
Gilchrist has been a regular scorer in his two seasons at Turf Moor since arriving from Manchester City as a 16-year-old in the summer of 2011 and Gallagher, who had a long wait last season for international clearance, has impressed this time round and has played for the Republic of Ireland at under-19 level.
Both will split their training for the rest of the season, spending some time with their loan club but also continuing their development under the youth coaches at Turf Moor.
Meanwhile, the club have now confirmed the medial ligament injury sustained by Tom Anderson playing for Hyde.
Manager Sean Dyche said: "He has got a knee injury but the good news is it's not as bad as we first thought. There was a worry that it might be a serious one. It's not, but it will take time. It's not a week or two. It's a longer rehabilitation period.
Anderson is now back at Burnley but Shay McCartan has extended his loan with Hyde until the end of the season.
Source: Clarets Mad