Flynn has made no secret of his desire to bolster his frontline and says owners Trivela are going above and beyond to help secure the necessary players.
Walsall, though, have missed out on another centre-forward target over the past week.
"Trivela have been very, very supportive. The problem we've got is that we've got a group of players out injured for three to six months," said Flynn.
"So, we've still got a budget, and I understand fully we stick to that budget.
"Will they be supportive and go over it? Yes, I think they will, because they've been that good.
"I can't speak highly enough of them. The striker search, me, Ben (Boycott), Matt (Jordan), Leigh (Pomlett), we're on it non-stop.
"We're looking for targets, identifying them.
"We've lost out on another one this week. There were a few rumours going around, but it is what it is. We're looking at the right players.
"I'm not going to sign somebody just because we need a striker.
"I want what I've got in my head. That will help the team. Otherwise, there's no point and you're just signing for the wrong reasons.
"It won't just be one. It'll be more than one, but we might have to be a little bit patient."
Flynn added on the search: "We've got to do what we have to do. It's an unfortunate situation because with the injuries, it's a juggling act.
"That's nobody's fault – not my fault, not the players' fault, Trivela's fault or Leigh's fault.
"We're in it together and will make sure we get it right."